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Practice book · Senior 5 · REB curriculum

Senior 5 Physics practice book

All 440 quiz questions in 11 units, with the correct answer and an explanation for each. Read a unit, then test yourself in the Senior 5 quiz.

Unit 1: Simple Harmonic Motion

Multiple choice

1.Which of the following correctly defines simple harmonic motion (SHM)?

  • AMotion in which acceleration is proportional to displacement and acts in the same direction as displacement
  • BMotion in which the restoring force is constant in magnitude and direction
  • CMotion in which acceleration is proportional to displacement and always directed towards a fixed equilibrium point
  • DMotion in which velocity is constant and directed towards a fixed point

Answer: C

SHM is defined by a = -ω²x: acceleration is proportional to displacement but always directed opposite to it, i.e. towards the equilibrium position.

Multiple choice

2.In SHM, the amplitude is best described as:

  • AThe maximum displacement of the particle from its equilibrium position
  • BThe time taken to complete one oscillation
  • CThe number of oscillations completed per second
  • DThe total distance travelled in one complete oscillation

Answer: A

Amplitude (A) is the maximum displacement from the equilibrium (mean) position.

Multiple choice

3.The period (T) and frequency (f) of an oscillation are related by:

  • AT = f
  • BT = 1/f
  • CT = 2f
  • DT = f²

Answer: B

Frequency is the reciprocal of the period: f = 1/T, so T = 1/f.

Multiple choice

4.In the equation x = A cos(ωt + φ), the quantity φ represents the:

  • AAmplitude
  • BAngular frequency
  • CPeriod
  • DPhase constant (initial phase)

Answer: D

φ is the phase constant, which fixes the state (position and direction of motion) of the oscillator at t = 0.

Multiple choice

5.Which of the following is the best real-life example of (approximately) simple harmonic motion?

  • AA stone falling freely under gravity
  • BA ball rolling down a straight incline
  • CA car accelerating uniformly from rest
  • DThe small-angle oscillation of a simple pendulum

Answer: D

For small angular displacements, a simple pendulum's restoring force is approximately proportional to displacement, giving SHM.

Multiple choice

6.In x = A cos(ωt + φ), the symbol ω represents the:

  • AAngular frequency
  • BLinear frequency
  • CPhase angle
  • DAmplitude

Answer: A

ω is the angular frequency, related to frequency by ω = 2πf, with units rad/s.

Multiple choice

7.A particle in SHM has amplitude 0.05 m and period 2 s. What is its maximum speed?

  • A0.079 m/s
  • B0.314 m/s
  • C0.025 m/s
  • D0.157 m/s

Answer: D

ω = 2π/T = 2π/2 = π rad/s. v_max = Aω = 0.05 × π ≈ 0.157 m/s.

Multiple choice

8.A particle executing SHM has angular frequency 4 rad/s. When its displacement is 0.02 m from equilibrium, its acceleration is:

  • A-1.28 m/s²
  • B-0.32 m/s²
  • C0.32 m/s²
  • D-0.08 m/s²

Answer: B

a = -ω²x = -(4)²(0.02) = -0.32 m/s²; the negative sign shows it is directed towards equilibrium.

Multiple choice

9.For a particle in SHM, the displacement–time graph is a cosine curve. The corresponding acceleration–time graph is:

  • AExactly in phase with the velocity graph
  • BA cosine curve inverted (180° out of phase) with displacement
  • CIn phase with the displacement graph
  • DA straight line

Answer: B

Since a = -ω²x, when x follows a cosine curve, a follows an inverted cosine curve — 180° (π rad) out of phase with displacement.

Multiple choice

10.In SHM, the velocity–time graph is out of phase with the displacement–time graph by:

  • A90°
  • B180°
  • C45°
  • D0°

Answer: A

Differentiating x = A cos(ωt+φ) gives v = -Aω sin(ωt+φ), which is a sine function — 90° out of phase with the cosine displacement.

Multiple choice

11.In SHM, at the equilibrium position (x = 0), the kinetic energy of the oscillator is:

  • AZero
  • BEqual to the potential energy
  • CMinimum but not zero
  • DMaximum

Answer: D

At x = 0 the speed is maximum (v_max = Aω), so kinetic energy is maximum there, while potential energy is zero.

Multiple choice

12.In SHM, the potential energy of the oscillator is maximum when:

  • AThe particle is at the extreme positions (x = ±A)
  • BThe particle is at the equilibrium position
  • CThe particle has maximum speed
  • DThe particle has zero acceleration

Answer: A

At the extremes x = ±A, velocity is zero and all the mechanical energy is stored as potential energy.

Multiple choice

13.The total mechanical energy of an undamped SHM oscillator, E = ½mω²A², is:

  • AMaximum only at x = ±A
  • BZero at all times
  • CMaximum only at x = 0
  • DConstant at all points of the motion

Answer: D

In the absence of damping, mechanical energy continuously converts between kinetic and potential forms but the total remains constant.

Multiple choice

14.A 0.2 kg mass oscillates in SHM with angular frequency 5 rad/s and amplitude 0.1 m. Its total mechanical energy is:

  • A0.25 J
  • B0.05 J
  • C0.025 J
  • D0.0125 J

Answer: C

E = ½mω²A² = 0.5 × 0.2 × 5² × 0.1² = 0.5 × 0.2 × 25 × 0.01 = 0.025 J.

Multiple choice

15.For an SHM oscillator of amplitude A, the kinetic energy when the displacement is x = A/2 is:

  • A3/4 of the total energy
  • BEqual to the total energy
  • C1/4 of the total energy
  • D1/2 of the total energy

Answer: A

KE = ½mω²(A²-x²) = ½mω²(A² - A²/4) = (3/4)(½mω²A²) = 3/4 of the total energy E.

Multiple choice

16.The period of a simple pendulum of length l at a place with gravitational acceleration g is given by:

  • AT = 2π√(g/l)
  • BT = 2π√(l/g)
  • CT = 2π(l/g)
  • DT = 2πl/g

Answer: B

The standard formula for the period of a simple pendulum (small oscillations) is T = 2π√(l/g).

Multiple choice

17.If the length of a simple pendulum is quadrupled while g stays constant, its period will:

  • AHalve
  • BQuadruple
  • CRemain the same
  • DDouble

Answer: D

Since T ∝ √l, quadrupling l multiplies T by √4 = 2, so the period doubles.

Multiple choice

18.A simple pendulum is taken to the Moon, where g is smaller than on Earth. Its period will:

  • AIncrease
  • BStay exactly the same
  • CBecome zero
  • DDecrease

Answer: A

Since T = 2π√(l/g), a smaller g gives a larger T, so the period increases on the Moon.

Multiple choice

19.The period of a mass–spring system with spring constant k and mass m is:

  • AT = 2π√(mk)
  • BT = 2π√(k/m)
  • CT = 2π√(m/k)
  • DT = 2πm/k

Answer: C

For a mass-spring oscillator, T = 2π√(m/k), derived from ω = √(k/m) and T = 2π/ω.

Multiple choice

20.If the spring constant of a mass–spring system is made 4 times larger while the mass is unchanged, the period becomes:

  • A4 times larger
  • BHalf of the original value
  • C2 times larger
  • DOne quarter of the original value

Answer: B

T ∝ 1/√k, so increasing k by a factor of 4 reduces T by a factor of √4 = 2, i.e. the period is halved.

Multiple choice

21.A mass-spring system has period 2 s and mass 0.5 kg. Its spring constant is approximately:

  • A9.87 N/m
  • B1.23 N/m
  • C4.93 N/m
  • D2.47 N/m

Answer: C

k = 4π²m/T² = 4π²(0.5)/(2²) = 4π²(0.5)/4 = π²(0.5) ≈ 4.93 N/m.

Multiple choice

22.For small oscillations, the period of a simple pendulum depends on:

  • AThe mass of the bob only
  • BThe length of the pendulum and gravitational acceleration only
  • CBoth the mass and the amplitude
  • DThe amplitude of swing only

Answer: B

T = 2π√(l/g) shows the period depends only on the length l and g, not on the mass of the bob or (for small angles) the amplitude.

Multiple choice

23.The fact that the period of a simple pendulum is (to a good approximation) independent of its amplitude, for small angles, is known as:

  • AIsochronism
  • BDamping
  • CSuperposition
  • DResonance

Answer: A

This property — equal periods regardless of (small) amplitude — is called isochronism.

Multiple choice

24.The relationship between angular frequency ω and frequency f is:

  • Aω = f/2π
  • Bω = 2πf
  • Cω = f
  • Dω = πf

Answer: B

Angular frequency ω = 2πf, since one full cycle (2π rad) corresponds to one period T = 1/f.

Multiple choice

25.A vibrating object has frequency 50 Hz. Its angular frequency is approximately:

  • A50 rad/s
  • B157 rad/s
  • C314 rad/s
  • D100 rad/s

Answer: C

ω = 2πf = 2π × 50 ≈ 314.16 rad/s.

Multiple choice

26.In x = A cos(ωt + φ), the quantity (ωt + φ) is called the:

  • AAngular frequency
  • BRestoring force
  • CAmplitude
  • DPhase of the motion

Answer: D

(ωt + φ) is the phase of the oscillation; it determines the exact state (position and direction) of the oscillator at time t.

Multiple choice

27.The restoring force in SHM is given by F = -kx. The negative sign shows that the force is:

  • AConstant in magnitude
  • BAlways directed towards the equilibrium position, opposing displacement
  • CIndependent of displacement
  • DAlways directed away from equilibrium

Answer: B

The negative sign indicates the restoring force always acts opposite to the displacement, pulling the particle back to equilibrium.

Multiple choice

28.A particle in SHM has amplitude 0.1 m and frequency 2 Hz. Its maximum acceleration is approximately:

  • A7.9 m/s²
  • B3.9 m/s²
  • C15.8 m/s²
  • D31.6 m/s²

Answer: C

ω = 2πf = 2π(2) ≈ 12.57 rad/s. a_max = ω²A = (12.57)² × 0.1 ≈ 15.8 m/s².

Multiple choice

29.The graph of acceleration (a) against displacement (x) for an SHM oscillator is:

  • AA straight line through the origin with negative slope
  • BA straight line through the origin with positive slope
  • CA parabola
  • DA sine curve

Answer: A

Since a = -ω²x, a plotted against x gives a straight line through the origin with slope -ω².

Multiple choice

30.Which of the following is NOT an example of (approximate) simple harmonic motion?

  • AA mass oscillating on an ideal spring
  • BA simple pendulum swinging through a small angle
  • CA ball rolling down a straight incline at constant acceleration
  • DThe vibration of a tuning fork prong

Answer: C

A ball rolling down an incline undergoes uniformly accelerated, non-oscillatory motion, so it is not SHM.

True or false

31.In SHM, the acceleration of the particle is always directed towards the equilibrium position.

Answer: True

This follows directly from a = -ω²x: acceleration and displacement are oppositely directed, i.e. acceleration points towards equilibrium.

True or false

32.The period of a simple pendulum depends on the mass of the bob.

Answer: False

T = 2π√(l/g) contains no mass term, so for an ideal simple pendulum the period is independent of the bob's mass.

True or false

33.At the extreme positions of an SHM oscillation, the kinetic energy of the particle is maximum.

Answer: False

At the extremes (x = ±A) the speed is zero, so kinetic energy is zero and potential energy is maximum there.

True or false

34.In the absence of damping, the total mechanical energy of an SHM oscillator remains constant throughout the motion.

Answer: True

With no resistive forces, energy simply converts between kinetic and potential forms, keeping the sum constant.

True or false

35.In SHM, the velocity and displacement of the particle are always exactly in phase with each other.

Answer: False

Velocity leads displacement by 90° (a quarter cycle), since v = -Aω sin(ωt+φ) while x = A cos(ωt+φ).

Fill in the blank

36.The maximum displacement of a particle from its equilibrium position during SHM is called the ______.

Answer: amplitude

By definition, amplitude (A) is the largest displacement reached from the equilibrium position.

Fill in the blank

37.The time taken by an oscillating particle to complete one full cycle of motion is called the ______.

Answer: period

The period (T) is the time for one complete oscillation.

Fill in the blank

38.In SHM, acceleration a = -ω²x shows that acceleration is directly proportional to ______ and directed towards the equilibrium point.

Answer: displacement

The defining relation of SHM is that acceleration is proportional to (and oppositely directed from) displacement.

Fill in the blank

39.The period of a simple pendulum is given by the formula T = 2π√(______).

Answer: l/g

T = 2π√(l/g), where l is the pendulum length and g is the acceleration due to gravity.

Fill in the blank

40.The period of a mass–spring system is given by the formula T = 2π√(______).

Answer: m/k

T = 2π√(m/k), where m is the oscillating mass and k is the spring constant.

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Unit 2: Damped and Forced Oscillations

Multiple choice

1.A damped oscillation is best described as one in which:

  • AThe amplitude increases steadily with time
  • BThe amplitude decreases progressively with time due to resistive forces
  • CThe period decreases to zero
  • DThe frequency increases with time

Answer: B

Damping is caused by resistive forces (friction, air resistance, viscosity) that remove energy from the system, so the amplitude decays with time.

Multiple choice

2.Which of the following is a real-life example of a damped oscillation?

  • AA car's suspension system settling after hitting a bump
  • BAn ideal pendulum swinging forever in a vacuum with no friction
  • CA perfectly elastic collision between two balls
  • DThe Earth orbiting the Sun

Answer: A

A car suspension oscillates and its amplitude dies away due to resistive (damping) forces from the shock absorber fluid.

Multiple choice

3.In a damped oscillator, the damping (resistive) force is generally modelled as being proportional to the object's:

  • ADisplacement
  • BMass only
  • CAcceleration
  • DVelocity

Answer: D

Damping forces (such as viscous drag) are typically proportional to velocity, F = -bv, where b is the damping coefficient.

Multiple choice

4.The differential equation describing a damped oscillator of mass m, damping coefficient b, and spring constant k is:

  • Ab(d²x/dt²) + m(dx/dt) = kx
  • Bm(d²x/dt²) - kx = 0
  • Cm(dx/dt) + kx² = 0
  • Dm(d²x/dt²) + b(dx/dt) + kx = 0

Answer: D

The damped oscillator equation includes an inertial term, a damping term proportional to velocity, and a restoring term proportional to displacement.

Multiple choice

5.For a lightly (under-) damped oscillator, the solution to the equation of motion has the general form:

  • Ax = A e^{bt}, an exponentially increasing displacement
  • Bx = A e^{-bt/2m} cos(ω't + φ), an oscillation with exponentially decaying amplitude
  • Cx = A cos(ωt + φ), a constant-amplitude oscillation
  • Dx = At, a linearly increasing displacement

Answer: B

Underdamped motion oscillates at a slightly reduced angular frequency ω' while its amplitude decays exponentially as e^{-bt/2m}.

Multiple choice

6.Which type of damping allows a displaced system to return to equilibrium in the shortest possible time without oscillating at all?

  • ACritical damping
  • BUnderdamping (light damping)
  • COverdamping (heavy damping)
  • DNo damping

Answer: A

Critical damping is the boundary case where the system returns to equilibrium as fast as possible without oscillating back and forth.

Multiple choice

7.An overdamped system, when displaced and released, will:

  • AOscillate with constant amplitude forever
  • BReturn to equilibrium slowly without any oscillation
  • COvershoot equilibrium many times before settling
  • DOscillate with slowly decreasing amplitude

Answer: B

In overdamping, resistive forces are so large that the system creeps back to equilibrium slowly and monotonically, without oscillating.

Multiple choice

8.In an underdamped (lightly damped) system, the displaced object:

  • AOscillates forever with constant amplitude
  • BOscillates back and forth several times with amplitude decreasing exponentially before coming to rest
  • CNever returns to the equilibrium position
  • DReturns to equilibrium in one smooth motion without oscillating

Answer: B

Underdamping is characterised by repeated oscillations whose amplitude decays exponentially with time until the system comes to rest.

Multiple choice

9.Which of the following is a good real-life example of a system deliberately designed to be critically (or near-critically) damped?

  • AA satellite orbiting the Earth
  • BA swing pushed by a child
  • CA guitar string left to vibrate freely
  • DA pointer/needle in an analogue galvanometer that must settle quickly without overshooting

Answer: D

Galvanometer needles and many measuring instrument pointers are designed close to critical damping so they settle on the correct reading quickly without oscillating.

Multiple choice

10.A door fitted with a hydraulic closer set too 'stiff' so that it closes very slowly without swinging back and forth is an example of:

  • AOverdamping
  • BResonance
  • CCritical damping
  • DUnderdamping

Answer: A

A very stiff closer that prevents any oscillation but closes sluggishly is exhibiting overdamped behaviour.

Multiple choice

11.In forced oscillations, once steady state is reached, the oscillating system vibrates at:

  • AZero frequency
  • BIts own natural frequency only
  • CA frequency exactly halfway between its natural frequency and the driving frequency
  • DThe frequency of the external (driving) force

Answer: D

After transients die away, a forced oscillator settles into vibrating at the same frequency as the periodic driving force applied to it.

Multiple choice

12.Resonance in a forced oscillating system occurs when:

  • AThe damping force is at its absolute maximum
  • BThe amplitude of the driving force is zero
  • CThe driving frequency is much greater than the natural frequency
  • DThe driving frequency equals the natural frequency of the system

Answer: D

Resonance occurs when the frequency of the applied periodic force matches the system's own natural frequency, producing maximum amplitude.

Multiple choice

13.At resonance, the amplitude of a forced oscillator is:

  • AAt its maximum value (for a given damping)
  • BIndependent of damping
  • CAt its minimum value
  • DZero

Answer: A

The amplitude–frequency response of a forced oscillator peaks sharply at (or near) the natural frequency, giving maximum amplitude at resonance.

Multiple choice

14.Regarding energy in a forced oscillation at steady state, which statement is correct?

  • AEnergy increases without limit indefinitely
  • BEnergy is only lost, never supplied
  • CThe energy supplied by the driving force per cycle equals the energy dissipated by damping per cycle
  • DNo energy is supplied by the driving force

Answer: C

At steady state the amplitude is constant, which requires the energy input from the driving force to exactly balance the energy dissipated by damping each cycle.

Multiple choice

15.The collapse of the Tacoma Narrows Bridge in 1940 is often cited as a dramatic real-life example of:

  • ASimple harmonic motion with no forcing
  • BOverdamping
  • CDestructive resonance
  • DCritical damping

Answer: C

Wind-induced periodic forces matched a natural vibration mode of the bridge, driving a resonant oscillation whose amplitude grew until the structure failed.

Multiple choice

16.In musical instruments such as a guitar, the hollow wooden body amplifies the sound of the vibrating string mainly because of:

  • AThe body absorbing all the vibrational energy
  • BCritical damping of the sound box
  • CResonance of the air/body cavity with the string's vibration
  • DOverdamping of the string

Answer: C

The body/air cavity has natural frequencies that resonate with the string's vibrations, reinforcing and amplifying the sound produced.

Multiple choice

17.Soldiers marching across a bridge are traditionally ordered to break step. This is done to avoid:

  • AIncreasing the bridge's natural frequency
  • BOverdamping the bridge
  • CReducing air resistance
  • DSetting up resonant vibrations that could dangerously amplify the bridge's oscillation

Answer: D

If the soldiers' marching frequency matched the bridge's natural frequency, resonance could build up dangerously large oscillations.

Multiple choice

18.Increasing the amount of damping in a forced oscillating system generally has what effect on the resonance peak?

  • AIt decreases the peak amplitude and broadens (flattens) the resonance curve
  • BIt increases the peak amplitude and sharpens the peak
  • CIt has no effect on the resonance curve at all
  • DIt shifts the resonant frequency to zero

Answer: A

More damping removes energy faster, reducing the maximum amplitude reached at resonance and broadening the frequency response curve.

Multiple choice

19.For a damped oscillator, which quantity decreases exponentially with time (while damped oscillation continues)?

  • AThe phase constant
  • BThe period
  • CThe amplitude
  • DThe angular frequency

Answer: C

In underdamped motion the amplitude envelope decays as A0 e^{-bt/2m}, while the angular frequency and period change only slightly.

Multiple choice

20.Compared with the natural (undamped) angular frequency ω0, the angular frequency ω' of a lightly damped oscillator is:

  • ASlightly greater than ω0
  • BExactly equal to ω0
  • CExactly double ω0
  • DSlightly less than ω0

Answer: D

Light damping slightly reduces the oscillation frequency: ω' = √(ω0² - (b/2m)²), which is a little less than ω0.

Multiple choice

21.In the damping equation m(d²x/dt²) + b(dx/dt) + kx = 0, the constant b represents the:

  • ADamping coefficient
  • BMass of the oscillator
  • CSpring constant
  • DNatural angular frequency

Answer: A

b is the damping coefficient, quantifying how strongly the resistive force opposes the motion.

Multiple choice

22.Car shock absorbers are generally designed to be close to which type of damping, to give a smooth ride that settles quickly without excessive bouncing?

  • AOverdamped only
  • BCritically damped
  • CUndamped
  • DUnderdamped only

Answer: B

Shock absorbers aim for near-critical damping: enough to quickly kill oscillations from bumps without making the ride harsh and sluggish.

Multiple choice

23.As the degree of light damping in an oscillator increases (while it remains underdamped), the period of oscillation:

  • ABecomes infinite
  • BIncreases slightly
  • CBecomes exactly zero
  • DDecreases significantly

Answer: B

Since ω' = √(ω0² - (b/2m)²) decreases as damping (b) increases, and T' = 2π/ω', the period slightly increases with more damping.

Multiple choice

24.The mechanical energy of a freely (unforced) damped oscillator, over time, will:

  • ADecrease continuously as it is dissipated as heat
  • BOscillate between two fixed non-zero values forever
  • CRemain exactly constant
  • DIncrease steadily

Answer: A

Damping forces continuously convert mechanical energy into heat (via friction/viscous drag), so the total energy of a freely damped oscillator falls with time.

Multiple choice

25.Which displacement–time graph best represents an underdamped oscillation?

  • AA curve that returns to zero in a single smooth motion with no oscillation
  • BA curve that rises smoothly to a peak and never returns to zero
  • CA curve that oscillates about zero with an amplitude that decays exponentially with time
  • DA straight horizontal line

Answer: C

Underdamped motion continues to oscillate about equilibrium, but with the peak amplitude shrinking exponentially over successive cycles.

Multiple choice

26.Compared to overdamping, critical damping brings a displaced system back to equilibrium:

  • AOnly after infinite time
  • BIn the shortest possible time, without oscillating
  • CMore slowly
  • DIn exactly the same time

Answer: B

Critical damping is defined as the smallest amount of damping that just prevents oscillation, giving the fastest return to equilibrium of the non-oscillatory cases.

Multiple choice

27.A pneumatic door closer adjusted so the door closes slowly and gently, without slamming or swinging back open, is behaving as a(n):

  • AOverdamped system
  • BUndamped system
  • CResonant system
  • DUnderdamped system

Answer: A

A door that creeps closed slowly with no oscillation, taking longer than the minimum possible time, is exhibiting overdamped behaviour.

Multiple choice

28.The natural (resonant) frequency of a simple mass–spring oscillator mainly depends on:

  • AThe driving force amplitude only
  • BThe colour of the spring
  • CThe mass and the stiffness (spring constant) of the system
  • DOnly the amplitude of oscillation

Answer: C

The natural angular frequency of a mass-spring system is ω0 = √(k/m), depending on stiffness k and mass m, not on amplitude.

Multiple choice

29.Which of these is NOT a genuine real-life example of resonance?

  • AA radio receiver tuned to pick up a particular broadcast frequency
  • BAn opera singer's voice shattering a wine glass at a matching frequency
  • CA ball slowly rolling to rest on a flat floor due to friction
  • DA child's swing rising higher when pushed at its natural frequency

Answer: C

A ball coming to rest due to friction is simple energy dissipation, not resonance, which specifically requires a periodic driving force matching a natural frequency.

Multiple choice

30.The amplitude of a lightly damped oscillator falls from 10 cm to 5 cm in 4 s. Using A = A0 e^{-λt}, the decay constant λ is approximately:

  • A0.693 s⁻¹
  • B0.173 s⁻¹
  • C0.087 s⁻¹
  • D0.347 s⁻¹

Answer: B

0.5 = e^{-4λ} ⟹ ln(0.5) = -4λ ⟹ λ = ln2/4 ≈ 0.693/4 ≈ 0.173 s⁻¹.

True or false

31.In forced oscillations, once steady state is reached, the system vibrates at the frequency of the driving force rather than its own natural frequency.

Answer: True

After initial transients die out, the oscillator locks onto and vibrates at the frequency of the applied periodic driving force.

True or false

32.A critically damped system oscillates back and forth several times before finally settling at its equilibrium position.

Answer: False

A critically damped system does not oscillate at all; it returns directly to equilibrium in the shortest possible time.

True or false

33.Resonance occurs when the frequency of the driving force equals the natural frequency of the oscillating system.

Answer: True

This matching of frequencies allows maximum energy transfer from the driving force to the oscillator, producing resonance.

True or false

34.An overdamped system returns to its equilibrium position faster than a critically damped system.

Answer: False

Critical damping gives the fastest non-oscillatory return to equilibrium; an overdamped system returns more slowly than this.

True or false

35.Damping always increases the amplitude of an oscillating system over time.

Answer: False

Damping removes energy from the system due to resistive forces, so it decreases (not increases) the amplitude over time.

Fill in the blank

36.In damped oscillations, mechanical energy is gradually converted into ______ due to resistive forces acting on the system.

Answer: heat

Resistive/frictional forces convert the ordered mechanical energy of oscillation into heat (and sound), dissipating it from the system.

Fill in the blank

37.A system that returns to equilibrium in the shortest possible time without oscillating is said to be ______ damped.

Answer: critically

This special boundary case between underdamping and overdamping is called critical damping.

Fill in the blank

38.The phenomenon in which a system driven at its natural frequency oscillates with a dramatically increased amplitude is called ______.

Answer: resonance

Resonance occurs when the driving frequency matches the natural frequency, maximising energy transfer and amplitude.

Fill in the blank

39.In an ______ oscillation, the object oscillates back and forth several times with an amplitude that decreases exponentially before coming to rest.

Answer: underdamped (lightly damped)

This is the underdamped (lightly damped) case, distinct from critical and overdamping, which show no oscillation.

Fill in the blank

40.The 1940 collapse of the Tacoma Narrows Bridge is a famous real-life example of destructive ______ caused by wind-induced forces.

Answer: resonance

Periodic wind forces matched a natural vibrational mode of the bridge, producing a resonant oscillation that grew until the structure failed.

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Unit 3: Propagation of Mechanical Waves

Multiple choice

1.A mechanical wave is best defined as a wave that:

  • ATravels only through empty space
  • BRequires a material medium (solid, liquid or gas) through which to propagate
  • CCan travel through a vacuum without any medium
  • DHas no wavelength or frequency

Answer: B

Unlike electromagnetic waves, mechanical waves need a material medium — such as air, water, or a solid — to transmit their energy.

Multiple choice

2.In a transverse wave, the particles of the medium vibrate:

  • AIn a direction that has no relation to the wave's motion
  • BParallel to the direction of wave propagation
  • CPerpendicular to the direction of wave propagation
  • DIn circles only, never in straight lines

Answer: C

In transverse waves (e.g. waves on a stretched string), particle displacement is at right angles to the direction the wave travels.

Multiple choice

3.In a longitudinal wave, the particles of the medium vibrate:

  • ANot at all; only the wave pattern itself moves
  • BIn a plane containing the wave crest only
  • CParallel to the direction of wave propagation, creating compressions and rarefactions
  • DPerpendicular to the direction of wave propagation

Answer: C

Longitudinal waves, such as sound in air, have particle motion along the same line as the direction of energy transfer, producing compressions and rarefactions.

Multiple choice

4.Which of the following is the best example of a longitudinal mechanical wave?

  • AA light wave travelling through glass
  • BA sound wave travelling through air
  • CA wave on the surface of water
  • DA wave travelling along a stretched rope

Answer: B

Sound waves involve air particles oscillating back and forth along the direction of propagation, making them longitudinal waves.

Multiple choice

5.For a progressive wave given by y = A sin(ωt - kx), the quantity k is called the:

  • APhase constant only
  • BAngular frequency
  • CAmplitude
  • DWave number, equal to 2π/λ

Answer: D

k is the wave number (or propagation constant), related to wavelength λ by k = 2π/λ.

Multiple choice

6.A progressive sound wave has frequency 256 Hz and wavelength 1.3 m. Its speed is approximately:

  • A1.3 m/s
  • B332.8 m/s
  • C197 m/s
  • D256 m/s

Answer: B

Using v = fλ: v = 256 × 1.3 ≈ 332.8 m/s, close to the typical speed of sound in air.

Multiple choice

7.A wave has wavelength 0.5 m. Its wave number k is approximately:

  • A12.57 rad/m
  • B3.14 rad/m
  • C0.5 rad/m
  • D6.28 rad/m

Answer: A

k = 2π/λ = 2π/0.5 ≈ 12.57 rad/m.

Multiple choice

8.A wave has a frequency of 100 Hz. Its angular frequency ω is approximately:

  • A200 rad/s
  • B100 rad/s
  • C628.3 rad/s
  • D314 rad/s

Answer: C

ω = 2πf = 2π × 100 ≈ 628.3 rad/s.

Multiple choice

9.In the wave equation y = A sin(ωt - kx), the constant A represents the:

  • AWave speed
  • BWavelength
  • CWave number
  • DAmplitude of the wave

Answer: D

A is the amplitude — the maximum displacement of a particle from its equilibrium position as the wave passes.

Multiple choice

10.Two points on a progressive wave are separated by a distance Δx along the direction of travel. Their phase difference Δφ is given by:

  • AΔφ = A·Δx
  • BΔφ = Δx/k
  • CΔφ = kΔx
  • DΔφ = ωΔx

Answer: C

Phase difference between two points a distance Δx apart is Δφ = kΔx, where k is the wave number.

Multiple choice

11.A distinguishing feature of a progressive (travelling) wave is that it:

  • ACannot be reflected
  • BTransfers matter but not energy along the medium
  • CHas fixed nodes that never move
  • DTransfers energy from one place to another without net transfer of matter

Answer: D

A progressive wave carries energy away from its source through the medium, while the medium's particles only oscillate about fixed positions — no net matter is transported.

Multiple choice

12.A stationary (standing) wave is formed when:

  • AA single wave travels through a medium without any reflection
  • BTwo waves of very different frequencies are combined
  • CTwo identical waves travelling in opposite directions superpose in the same medium
  • DA wave loses all of its energy to friction

Answer: C

Standing waves arise from the superposition of two coherent waves of equal amplitude and frequency travelling in opposite directions, e.g. an incident wave and its reflection.

Multiple choice

13.Which of the following best represents the equation of a stationary wave formed on a string?

  • Ay = A + kx, a linear function of position
  • By = A sin(ωt - kx), representing a wave travelling in the +x direction
  • Cy = A e^{-kx}, an exponentially decaying displacement
  • Dy = 2A sin(kx) cos(ωt), with amplitude 2A sin(kx) varying with position but no wave travelling

Answer: D

A stationary wave's displacement can be written as y = 2A sin(kx) cos(ωt): each point oscillates in time with an amplitude that depends on its fixed position x, and the pattern does not travel.

Multiple choice

14.In a stationary wave, points that remain permanently at rest (zero displacement at all times) are called:

  • ATroughs
  • BAntinodes
  • CNodes
  • DCrests

Answer: C

Nodes are the fixed points of zero amplitude in a standing wave pattern.

Multiple choice

15.In a stationary wave, points of maximum amplitude of vibration are called:

  • AAntinodes
  • BRarefactions
  • CNodes
  • DWavefronts

Answer: A

Antinodes are the points where the standing wave amplitude is greatest.

Multiple choice

16.The distance between two adjacent nodes in a stationary wave is:

  • Aλ/2
  • Bλ (one full wavelength)
  • Cλ/4
  • D2λ

Answer: A

Adjacent nodes in a standing wave pattern are separated by half a wavelength, λ/2.

Multiple choice

17.The distance between a node and the nearest adjacent antinode in a stationary wave is:

  • Aλ/4
  • Bλ
  • C3λ/4
  • Dλ/2

Answer: A

A node and its neighbouring antinode are always a quarter wavelength (λ/4) apart.

Multiple choice

18.A string of length L is fixed at both ends and vibrates in its fundamental (first harmonic) mode. The wavelength of this mode is:

  • Aλ = 2L
  • Bλ = L/2
  • Cλ = 4L
  • Dλ = L

Answer: A

The fundamental mode of a string fixed at both ends has a node at each end and one antinode in the middle, fitting half a wavelength into L, so λ = 2L.

Multiple choice

19.For a string of length L and wave speed v fixed at both ends, the fundamental frequency is given by:

  • Af1 = v/2L
  • Bf1 = 2v/L
  • Cf1 = vL/2
  • Df1 = v/L

Answer: A

Since λ1 = 2L for the fundamental mode, f1 = v/λ1 = v/(2L).

Multiple choice

20.A string of length 0.6 m has wave speed 300 m/s along it. Its fundamental frequency of vibration is:

  • A180 Hz
  • B250 Hz
  • C500 Hz
  • D125 Hz

Answer: B

f1 = v/(2L) = 300/(2 × 0.6) = 300/1.2 = 250 Hz.

Multiple choice

21.For a stretched string fixed at both ends, the wavelength of the second harmonic (first overtone) is related to the string length L by:

  • Aλ2 = L
  • Bλ2 = 4L
  • Cλ2 = 2L
  • Dλ2 = L/2

Answer: A

The second harmonic has one extra node compared to the fundamental, fitting a full wavelength into the string, so λ2 = L.

Multiple choice

22.Regarding energy transfer, a stationary wave differs from a progressive wave in that a stationary wave:

  • ATransfers matter but no energy
  • BStores energy locally, oscillating between kinetic and potential forms, with no net energy transfer along the medium
  • CCannot store any energy at all
  • DTransfers energy steadily from one end of the medium to the other

Answer: B

In a standing wave, energy is confined between nodes and antinodes, oscillating in place rather than propagating steadily along the medium as in a travelling wave.

Multiple choice

23.Which of the following is a good real-life example of a stationary (standing) wave?

  • AA single pulse travelling once along a rope
  • BRipples spreading outward from a stone dropped in a pond
  • CSound travelling directly from a loudspeaker to a listener's ear
  • DA vibrating guitar or violin string fixed at both ends

Answer: D

The fixed ends of a vibrating string reflect waves, and the incident and reflected waves superpose to form a stable standing wave pattern.

Multiple choice

24.Which of the following is a good real-life example of a progressive (travelling) wave?

  • AThe fixed nodes on a vibrating rope tied at both ends
  • BThe stationary pattern on a plucked guitar string
  • CA standing wave in an organ pipe closed at one end
  • DSound travelling outward from a loudspeaker to a listener

Answer: D

Sound spreading from a source to a listener is a classic progressive wave: it carries energy through the air from one place to another.

Multiple choice

25.For the wave equation y = A sin(ωt - kx), the negative sign before kx indicates that the wave travels:

  • AIn the negative x-direction
  • BIt does not indicate any direction
  • CIn a circular path
  • DIn the positive x-direction

Answer: D

The form y = A sin(ωt - kx) represents a wave moving in the positive x-direction; y = A sin(ωt + kx) would represent motion in the negative x-direction.

Multiple choice

26.The wave speed (v), wavelength (λ) and period (T) of a progressive wave are related by:

  • Av = λ + T
  • Bv = λT
  • Cv = λ/T
  • Dv = T/λ

Answer: C

Since the wave moves one wavelength in one period, its speed is v = λ/T (equivalently v = fλ).

Multiple choice

27.Sound waves travelling through air are classified as:

  • AStanding waves only
  • BLongitudinal waves
  • CElectromagnetic waves
  • DTransverse waves

Answer: B

Sound propagates through air via alternating compressions and rarefactions, with particle motion parallel to the direction of travel — a longitudinal wave.

Multiple choice

28.Regarding water surface waves, which statement is most accurate?

  • AThey are purely longitudinal, with particles moving strictly forward and backward
  • BWater particles typically move in roughly circular/elliptical paths, showing a combination of transverse and longitudinal motion
  • CWater particles do not move at all as the wave passes
  • DThey are purely transverse, with particles moving strictly up and down

Answer: B

In real water waves, particles near the surface trace approximately circular or elliptical orbits, combining both transverse (vertical) and longitudinal (horizontal) components of motion.

Multiple choice

29.A progressive wave is described by y = 0.02 sin(4πt - 2πx) (SI units). The speed of this wave is:

  • A0.5 m/s
  • B2 m/s
  • C1 m/s
  • D4 m/s

Answer: B

Comparing with y = A sin(ωt - kx): ω = 4π rad/s and k = 2π rad/m, so v = ω/k = 4π/2π = 2 m/s.

Multiple choice

30.A wave in air has frequency 50 Hz and travels at the speed of sound, 340 m/s. Its wavelength is:

  • A6.8 m
  • B5.0 m
  • C3.4 m
  • D17,000 m

Answer: A

λ = v/f = 340/50 = 6.8 m.

True or false

31.Mechanical waves cannot travel through a vacuum because they require a material medium.

Answer: True

Mechanical waves rely on the oscillation of particles in a medium, so unlike electromagnetic waves, they cannot propagate through a vacuum.

True or false

32.In a transverse wave, particles of the medium move parallel to the direction of wave propagation.

Answer: False

That description applies to longitudinal waves; in a transverse wave particles move perpendicular to the direction of propagation.

True or false

33.A stationary wave transfers energy steadily from one end of the medium to the other, just like a progressive wave.

Answer: False

A stationary wave stores energy locally between nodes and antinodes; there is no net energy transfer along the medium.

True or false

34.The distance between two consecutive nodes in a stationary wave is equal to half a wavelength.

Answer: True

Consecutive nodes are always separated by λ/2 in a standing wave pattern.

True or false

35.Sound waves travelling through air are longitudinal waves.

Answer: True

Air particles oscillate back and forth parallel to the direction sound travels, producing compressions and rarefactions typical of longitudinal waves.

Fill in the blank

36.A wave that requires a material medium in order to travel is called a ______ wave.

Answer: mechanical

Mechanical waves (unlike electromagnetic waves) need a medium such as a solid, liquid or gas to propagate.

Fill in the blank

37.In a ______ wave, the particles of the medium vibrate perpendicular to the direction the wave travels.

Answer: transverse

This perpendicular relationship between particle motion and wave direction defines a transverse wave.

Fill in the blank

38.Points on a stationary wave pattern that remain permanently at rest are called ______.

Answer: nodes

Nodes are fixed points of zero displacement formed by destructive interference in a standing wave.

Fill in the blank

39.The general equation of a progressive wave travelling in the positive x-direction is y = A sin(______).

Answer: ωt - kx

The term (ωt - kx) represents the phase of a wave moving in the positive x-direction; the standard form is y = A sin(ωt - kx).

Fill in the blank

40.A stationary wave is produced by the superposition of two identical waves of the same frequency and amplitude travelling in ______ directions.

Answer: opposite

It is the meeting of an incident wave and its reflection, travelling in opposite directions, that produces a standing wave pattern.

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Unit 4: Fluid Mechanics

Multiple choice

1.The pressure P at a depth h below the surface of a liquid of density ρ (taking g as the acceleration due to gravity) is given by:

  • AP = hρg
  • BP = h + ρg
  • CP = h²ρg
  • DP = h/(ρg)

Answer: A

The pressure due to a liquid column is P = hρg, which increases linearly with depth h and with density ρ.

Multiple choice

2.Using g = 10 m/s², the pressure at a depth of 10 m in water (density 1000 kg/m³) is:

  • A1 × 10⁴ Pa
  • B1 × 10⁶ Pa
  • C1 × 10⁵ Pa
  • D1 × 10³ Pa

Answer: C

P = hρg = 10 × 1000 × 10 = 100,000 Pa = 1 × 10⁵ Pa.

Multiple choice

3.Pascal's principle states that:

  • APressure applied to an enclosed fluid is transmitted equally to every part of the fluid and to the walls of its container
  • BFluids cannot transmit pressure at all
  • CPressure in a fluid decreases with increasing depth
  • DPressure in a moving fluid is always constant

Answer: A

Pascal's principle is the basis of hydraulic systems: pressure applied anywhere in an enclosed, incompressible fluid is transmitted undiminished throughout the fluid.

Multiple choice

4.In a hydraulic lift, a force of 50 N is applied to a small piston of area 0.001 m², and the load is on a large piston of area 0.1 m². The force the large piston can support is:

  • A500 N
  • B50 N
  • C5,000 N
  • D50,000 N

Answer: C

Pressure is transmitted equally: F1/A1 = F2/A2 ⟹ F2 = F1 × (A2/A1) = 50 × (0.1/0.001) = 5,000 N.

Multiple choice

5.The rise (or fall) of a liquid in a narrow tube due to surface tension effects is called:

  • ATurbulence
  • BBuoyancy
  • CCapillarity
  • DViscosity

Answer: C

Capillarity describes the rise or depression of a liquid surface inside a narrow (capillary) tube, caused by surface tension and adhesive/cohesive forces.

Multiple choice

6.The height of capillary rise h in a tube of radius r, for a liquid of surface tension T, density ρ, and contact angle θ, is given by:

  • Ah = Tρg/(2rcosθ)
  • Bh = rρg/(2Tcosθ)
  • Ch = 2T/(rρgcosθ)
  • Dh = 2Tcosθ/(rρg)

Answer: D

The standard capillary rise formula is h = 2Tcosθ/(rρg).

Multiple choice

7.According to the capillary rise formula, if the radius of the capillary tube is decreased (all else constant), the height of liquid rise will:

  • ADecrease
  • BBecome negative
  • CIncrease
  • DRemain unchanged

Answer: C

Since h ∝ 1/r, a narrower tube produces a greater capillary rise.

Multiple choice

8.Capillary depression (the liquid surface being pushed down in a narrow tube) occurs typically when:

  • AThe liquid completely wets the tube material (contact angle less than 90°)
  • BThe tube is extremely wide
  • CThe liquid has zero surface tension
  • DThe liquid does not wet the tube material (contact angle greater than 90°), as with mercury in a glass tube

Answer: D

When adhesive forces between liquid and tube are weaker than cohesive forces within the liquid (contact angle > 90°), the liquid is depressed rather than raised, as seen with mercury in glass.

Multiple choice

9.The SI unit of surface tension is:

  • AN/m
  • BN·m
  • CPa·s
  • DN/m²

Answer: A

Surface tension is force per unit length acting along a line on the liquid surface, so its SI unit is newton per metre (N/m).

Multiple choice

10.The Reynolds number for flow of a fluid of density ρ and viscosity η, moving with speed v through a pipe of diameter d, is given by:

  • ARe = ηv d/ρ
  • BRe = ρvd/η
  • CRe = vd/(ρη)
  • DRe = ρη/(vd)

Answer: B

The Reynolds number is defined as Re = ρvd/η, a dimensionless number comparing inertial to viscous forces in the flow.

Multiple choice

11.A low Reynolds number for fluid flow in a pipe generally indicates:

  • ATurbulent flow
  • BNo flow at all
  • CFlow at the speed of sound
  • DLaminar (smooth, streamline) flow

Answer: D

Low Reynolds numbers correspond to viscous forces dominating over inertial forces, favouring smooth, orderly laminar flow.

Multiple choice

12.A high Reynolds number for fluid flow generally indicates:

  • AFlow that has completely stopped
  • BLaminar flow
  • CTurbulent, chaotic flow with eddies and mixing
  • DZero viscosity of the fluid

Answer: C

At high Reynolds numbers, inertial forces dominate, and small disturbances grow into chaotic eddies, producing turbulent flow.

Multiple choice

13.The continuity equation A1v1 = A2v2 for an incompressible fluid expresses the principle of:

  • AConservation of pressure
  • BConservation of mass (volume flow rate is constant)
  • CConservation of energy
  • DConservation of momentum

Answer: B

Since the fluid is incompressible and cannot accumulate anywhere in a pipe, the volume flow rate (Av) must be the same at every cross-section — this is conservation of mass.

Multiple choice

14.Water flows through a pipe that narrows from area 0.02 m² to 0.01 m². If the speed in the wider section is 3 m/s, the speed in the narrower section is:

  • A1.5 m/s
  • B3 m/s
  • C6 m/s
  • D12 m/s

Answer: C

By continuity, A1v1 = A2v2 ⟹ v2 = (A1v1)/A2 = (0.02 × 3)/0.01 = 6 m/s.

Multiple choice

15.Bernoulli's equation, P + ½ρv² + ρgh = constant, along a streamline represents:

  • AThe Reynolds number of the flow
  • BConservation of mass only
  • CConservation of electric charge in a moving fluid
  • DConservation of mechanical energy per unit volume for an ideal, incompressible, non-viscous fluid

Answer: D

Bernoulli's equation is essentially the work-energy theorem applied to fluid flow, stating that pressure energy, kinetic energy and potential energy per unit volume sum to a constant along a streamline.

Multiple choice

16.According to Bernoulli's principle, in a horizontal flow where the fluid speed increases, the pressure of the fluid:

  • AStays exactly constant
  • BBecomes negative always
  • CIncreases
  • DDecreases

Answer: D

For horizontal flow, P + ½ρv² = constant, so an increase in speed v must be accompanied by a decrease in pressure P.

Multiple choice

17.The lift on an aircraft wing is commonly explained using Bernoulli's principle by noting that:

  • AAir moves faster over the curved upper surface than beneath, creating lower pressure above and a net upward force
  • BAir moves slower over the top of the wing, creating higher pressure there
  • CAir pressure is the same above and below the wing, so no lift is generated
  • DThe wing simply pushes air downward with no pressure difference involved

Answer: A

The wing's shape causes air to travel faster over the curved top, lowering the pressure there relative to beneath the wing, producing an upward lift force.

Multiple choice

18.A perfume atomizer (spray bottle) works by using a rapid stream of air blown across the top of a narrow tube, which:

  • AIncreases the pressure at the top of the tube, pushing the perfume back down
  • BFreezes the liquid perfume so it cannot flow
  • CHas no effect on pressure inside the tube
  • DDecreases the pressure at the top of the tube (Bernoulli's principle), drawing the liquid perfume up the tube to be sprayed

Answer: D

The fast airstream over the tube's opening lowers the local pressure there, so atmospheric pressure on the liquid pushes it up the tube where it is atomised into a fine spray.

Multiple choice

19.In a carburettor, a narrow constriction (venturi) in the air passage is used to:

  • AIncrease air pressure so fuel is pushed away from the air stream
  • BSpeed up the air flow, lowering local pressure so that fuel is drawn in and mixed with the air
  • CCool the incoming air to increase its density
  • DStop the flow of air completely

Answer: B

The venturi constriction increases air speed and lowers pressure there, drawing fuel from the fuel jet into the fast-moving airstream — a direct application of Bernoulli's principle.

Multiple choice

20.A laboratory filter pump (aspirator) removes air from a flask using:

  • AHeating the flask to boil off the air
  • BA fast jet of water passing through a constriction, creating low pressure that sucks in air from the side tube
  • CA rotating fan blade placed inside the flask
  • DIncreasing the pressure of water flowing past the flask

Answer: B

As water is forced through a narrowing nozzle, its speed increases and pressure drops (Bernoulli's principle), so air is drawn in and carried away with the water stream.

Multiple choice

21.Sailing boats can make progress even when sailing partly against the wind mainly because:

  • AThe sail acts like an airfoil, and air flowing faster over its curved leeward side lowers pressure there, producing a forward-driving force component
  • BWind always pushes the boat directly backward, so no forward motion is possible
  • CWater pressure alone propels the boat forward
  • DThe sail has no aerodynamic effect at all

Answer: A

A well-trimmed sail behaves like an aircraft wing: air moves faster over its curved side, lowering pressure there and generating a net force with a usable forward component, allowing tacking against the wind.

Multiple choice

22.Terminal velocity of an object falling through a viscous fluid is reached when:

  • AThe net force on the object becomes zero, so weight is balanced by drag and upthrust
  • BThe object's acceleration is at its maximum
  • CThe viscosity of the fluid becomes zero
  • DThe object stops moving completely

Answer: A

At terminal velocity, the downward weight is exactly balanced by the upward viscous drag and buoyant upthrust, giving zero net force and zero acceleration, so the velocity stays constant.

Multiple choice

23.By Stokes' law, the terminal velocity v_t of a small sphere of radius r, density ρ, falling through a fluid of density σ and viscosity η is given by:

  • Av_t = 2r²g(ρ - σ)/(9η)
  • Bv_t = 9η/(2r²g(ρ - σ))
  • Cv_t = 2rg(ρ - σ)/(9η)
  • Dv_t = r²g(ρ + σ)/(9η)

Answer: A

Stokes' law gives the terminal velocity of a small sphere in a viscous fluid as v_t = 2r²g(ρ - σ)/(9η).

Multiple choice

24.At the instant an object reaches terminal velocity while falling through a fluid, its acceleration is:

  • ANegative and increasing in magnitude
  • BZero
  • CEqual to g
  • DMaximum

Answer: B

Terminal velocity is, by definition, the constant final velocity reached once the net force (and hence acceleration) on the falling object becomes zero.

Multiple choice

25.The velocity–time graph of an object released from rest and falling through a viscous fluid typically shows:

  • AVelocity that is constant from the very start
  • BVelocity increasing rapidly at first, then levelling off asymptotically to a constant terminal velocity
  • CVelocity decreasing steadily to zero
  • DVelocity increasing linearly forever with no limit

Answer: B

The object accelerates from rest, but as speed increases, drag increases too, so acceleration decreases and velocity approaches (but never quite reaches, in theory) a constant terminal value.

Multiple choice

26.The SI unit of dynamic viscosity (η) is:

  • AN/m
  • Bm²/s only
  • Ckg/m³
  • DPa·s (equivalently N·s/m²)

Answer: D

Dynamic viscosity has SI units of pascal-seconds (Pa·s), equivalent to N·s/m².

Multiple choice

27.If the viscosity of the fluid increases while all other factors (radius, densities, g) remain constant, the terminal velocity of a falling sphere will:

  • AIncrease
  • BBecome infinite
  • CDecrease
  • DStay exactly the same

Answer: C

Since v_t = 2r²g(ρ-σ)/(9η), terminal velocity is inversely proportional to viscosity η, so increasing η decreases v_t.

Multiple choice

28.If the radius of a falling sphere is doubled while everything else stays the same, its terminal velocity (by Stokes' law) becomes:

  • AHalf as large
  • BFour times as large
  • CThe same
  • DTwice as large

Answer: B

Since v_t ∝ r², doubling the radius increases the terminal velocity by a factor of 2² = 4.

Multiple choice

29.Water flows horizontally through a pipe that narrows so its speed increases from 1 m/s to 4 m/s. If the pressure in the wide section is 200,000 Pa and the density of water is 1000 kg/m³, the pressure in the narrow section is approximately:

  • A192,500 Pa
  • B207,500 Pa
  • C200,000 Pa
  • D185,500 Pa

Answer: A

By Bernoulli's equation for horizontal flow: P1 + ½ρv1² = P2 + ½ρv2². P2 = 200,000 + ½(1000)(1² - 4²) = 200,000 + 500(1-16) = 200,000 - 7,500 = 192,500 Pa.

Multiple choice

30.Which of the following does NOT directly affect the height of capillary rise in a tube, according to h = 2Tcosθ/(rρg)?

  • AThe density of the liquid
  • BThe overall length of the tube (provided it is long enough)
  • CThe radius of the tube
  • DThe surface tension of the liquid

Answer: B

The capillary rise formula contains T, θ, r, ρ and g, but not the total length of the tube, so as long as the tube is long enough, its length does not affect the rise height.

True or false

31.The pressure at a point within a liquid increases as the depth below the surface increases.

Answer: True

Since P = hρg, pressure grows linearly with depth h for a given liquid.

True or false

32.Pascal's principle applies only to gases and cannot be applied to liquids in hydraulic systems.

Answer: False

Pascal's principle applies to enclosed fluids in general, and it is precisely the basis of hydraulic liquid systems such as hydraulic jacks and presses.

True or false

33.A high Reynolds number for fluid flow through a pipe generally indicates turbulent flow.

Answer: True

High Reynolds numbers mean inertial forces dominate viscous forces, favouring the onset of chaotic, turbulent flow.

True or false

34.According to Bernoulli's principle, an increase in a fluid's speed along a horizontal streamline is accompanied by an increase in its pressure.

Answer: False

Bernoulli's principle states the opposite: for horizontal flow, an increase in speed is accompanied by a decrease in pressure, since P + ½ρv² is constant.

True or false

35.An object falling through a viscous fluid reaches terminal velocity when the net force acting on it becomes zero.

Answer: True

At terminal velocity, weight is exactly balanced by drag and upthrust, giving zero net force and constant velocity.

Fill in the blank

36.The pressure exerted at a depth h in a liquid of density ρ is given by the formula P = ______.

Answer: hρg

This formula shows that liquid pressure depends on the depth, the liquid's density, and gravitational acceleration.

Fill in the blank

37.______'s principle states that pressure applied to an enclosed fluid is transmitted equally to every part of the fluid.

Answer: Pascal

This principle underlies hydraulic machines such as hydraulic lifts, jacks and brakes.

Fill in the blank

38.The rise or fall of a liquid surface inside a narrow tube due to surface tension is called ______.

Answer: capillarity

Capillarity results from the balance between adhesive forces (liquid–tube) and cohesive forces (within the liquid) combined with surface tension.

Fill in the blank

39.The equation A1v1 = A2v2, which expresses conservation of mass for an incompressible fluid in a pipe, is called the ______ equation.

Answer: continuity

This equation states that the volume flow rate (Av) is constant along a pipe of varying cross-sectional area.

Fill in the blank

40.The constant maximum velocity reached by an object falling through a viscous fluid, when the net force on it is zero, is called ______ velocity.

Answer: terminal

Terminal velocity occurs once weight is balanced exactly by the fluid's drag and upthrust forces.

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Unit 5: Motion on Orbits

Multiple choice

1.Newton's law of universal gravitation states that the gravitational force between two point masses is

  • Adirectly proportional to the product of the masses and inversely proportional to their separation
  • Binversely proportional to the product of the masses and directly proportional to the square of their separation
  • Cdirectly proportional to the sum of the masses and inversely proportional to their separation
  • Ddirectly proportional to the product of the masses and inversely proportional to the square of their separation

Answer: D

F = Gm1m2/r², so F is proportional to m1m2 and inversely proportional to r².

Fill in the blank

2.The universal gravitational constant G has an approximate value of ______ N·m²/kg².

Answer: 6.67 × 10⁻¹¹

G = 6.67 × 10⁻¹¹ N m² kg⁻² is the constant of proportionality in Newton's law of gravitation.

Multiple choice

3.Two point masses of 1000 kg and 500 kg have their centres 2.0 m apart. What is the gravitational force between them?

  • A3.34 × 10⁻⁵ N
  • B8.34 × 10⁻⁴ N
  • C1.67 × 10⁻⁵ N
  • D8.34 × 10⁻⁶ N

Answer: D

F = Gm1m2/r² = (6.67×10⁻¹¹ × 1000 × 500)/2² = (3.335×10⁻⁵)/4 = 8.34×10⁻⁶ N.

True or false

4.The gravitational force between two masses is always attractive, never repulsive.

Answer: True

Unlike electric charges, mass has only one 'sign', so gravity is always an attractive force.

Multiple choice

5.If the distance between two masses is doubled while the masses stay constant, the gravitational force between them

  • Adoubles
  • Bdecreases to one half of its original value
  • Cremains unchanged
  • Ddecreases to one quarter of its original value

Answer: D

F is proportional to 1/r², so doubling r reduces F by a factor of 2² = 4.

Multiple choice

6.Gravitational field strength at a point is defined as

  • Athe gravitational potential energy per unit mass at that point
  • Bthe gravitational force experienced per unit mass placed at that point
  • Cthe work done in moving a unit mass to infinity
  • Dthe gravitational force between two unit masses at that point

Answer: B

Field strength g = F/m, the force per unit mass placed at the point, measured in N/kg.

Fill in the blank

7.Gravitational field strength is measured in units of ______.

Answer: N/kg (equivalent to m/s²)

Since g = F/m, its SI unit is newtons per kilogram, which is dimensionally equivalent to m/s².

Multiple choice

8.The gravitational field strength at a distance r from a point mass M is given by

  • Ag = GM/r²
  • Bg = GM/r
  • Cg = GM²/r
  • Dg = GMr²

Answer: A

Combining F = GMm/r² with g = F/m gives g = GM/r².

Multiple choice

9.In a diagram of a gravitational field around an isolated spherical mass, the field lines

  • Apoint radially outward away from the mass
  • Bform closed loops around the mass
  • Crun parallel to each other in one fixed direction everywhere
  • Dpoint radially inward towards the centre of the mass

Answer: D

Gravitational field lines always point in the direction a small test mass would be pulled, i.e. towards the source mass.

Multiple choice

10.Which of the following is NOT a typical effect of the Earth's gravitational field?

  • AIt keeps the Moon and satellites in orbit
  • BIt causes the tides through the Moon's and Sun's gravitational pull
  • CIt causes electric charges to move between conductors
  • DIt gives objects weight

Answer: C

Movement of charge between conductors is an electrical effect, not gravitational; weight, orbits and tides are all gravitational effects.

Multiple choice

11.How does the acceleration due to gravity, g, vary with height h above the Earth's surface (radius R, surface value g₀)?

  • Ag = g₀(1 − h/R)
  • Bg stays constant with height
  • Cg = g₀R²/(R + h)²
  • Dg = g₀(R + h)²/R²

Answer: C

Since g = GM/r², replacing r with (R+h) gives g(h) = GM/(R+h)² = g₀R²/(R+h)², a decrease with height.

Multiple choice

12.A satellite orbits at a height above the Earth's surface equal to the Earth's radius R (so r = 2R). The gravitational acceleration there is

  • Ag₀
  • Bg₀/4
  • Cg₀/2
  • Dg₀/√2

Answer: B

g = g₀R²/(2R)² = g₀R²/4R² = g₀/4.

Multiple choice

13.Assuming the Earth has uniform density, how does g vary with depth d below the surface (radius R)?

  • Ag increases linearly with depth
  • Bg = g₀(R − d)²/R²
  • Cg = g₀(1 − d/R)
  • Dg = g₀R²/(R − d)²

Answer: C

Below the surface, only the mass enclosed within radius (R−d) contributes; for uniform density this gives g = g₀(1 − d/R), a linear decrease.

Multiple choice

14.At a depth equal to half the Earth's radius (assuming uniform density), the value of g is

  • A3g₀/4
  • Bg₀
  • Cg₀/4
  • Dg₀/2

Answer: D

g = g₀(1 − d/R) = g₀(1 − 0.5) = g₀/2.

True or false

15.Assuming uniform Earth density, the acceleration due to gravity decreases linearly to zero as you approach the Earth's centre.

Answer: True

For a uniform sphere, g = g₀(1 − d/R), which is a straight-line decrease reaching zero at d = R (the centre).

True or false

16.The acceleration due to gravity is at its maximum value exactly at the Earth's centre.

Answer: False

At the centre, the enclosed mass pulling in any one direction is effectively zero by symmetry, so g = 0 there; g is maximum at the surface.

Fill in the blank

17.The gravitational acceleration at the Earth's surface has an average value of approximately ______ m/s².

Answer: 9.8

The standard value used for g at the Earth's surface is 9.8 m/s² (sometimes taken as 9.81 m/s²).

Multiple choice

18.A mountaineer climbs to the top of a high mountain. Compared to sea level, their weight at the summit is

  • Aslightly more, because they are farther from the Earth's centre
  • Bexactly the same, since mass does not change
  • Cslightly less, because they are farther from the Earth's centre
  • Dzero, since gravity does not act above sea level

Answer: C

Increasing r decreases g = GM/r², so the gravitational force (weight) is slightly smaller at altitude, even though mass is unchanged.

Multiple choice

19.Deep in a mine shaft below the Earth's surface, the value of g compared to its surface value is

  • Asmaller
  • Blarger
  • Czero everywhere below the surface
  • Dexactly equal

Answer: A

Below the surface, less mass is enclosed within the radius to the point, so g decreases with depth (for a roughly uniform-density Earth).

Multiple choice

20.A satellite moves in a circular orbit of radius r around the Earth (mass M). Equating gravitational force to centripetal force gives an orbital speed of

  • Av = √(GM/r)
  • Bv = GM/r²
  • Cv = √(GMr)
  • Dv = GM/r

Answer: A

GMm/r² = mv²/r leads to v² = GM/r, so v = √(GM/r).

Multiple choice

21.For a satellite in circular orbit, Kepler's third law relates the orbital period T and orbital radius r as

  • AT ∝ r²
  • BT ∝ r³
  • CT² ∝ r³
  • DT² ∝ r

Answer: C

From GMm/r² = m(4π²/T²)r, we get T² = 4π²r³/GM, i.e. T² ∝ r³.

Multiple choice

22.The time period of a satellite in a circular orbit of radius r about the Earth (mass M) is given by

  • AT = 2π√(r³/GM)
  • BT = 2πr/√(GM)
  • CT = 2π√(r/GM)
  • DT = 2π√(GM/r³)

Answer: A

Derived from T² = 4π²r³/(GM): T = 2π√(r³/GM).

True or false

23.The orbital period of a satellite around the Earth depends on the mass of the satellite itself.

Answer: False

In T² = 4π²r³/GM, the satellite's own mass cancels out; the period depends only on orbital radius r and the Earth's mass M.

Multiple choice

24.A geostationary satellite is one that

  • Ahas the shortest possible orbital period of any satellite
  • Borbits in the equatorial plane with a period of 24 hours, appearing stationary relative to a point on Earth
  • Corbits over the poles once every hour
  • Dremains stationary in space while the Earth rotates beneath it

Answer: B

A geostationary satellite orbits in the equatorial plane, moving in the same direction as Earth's rotation with a period equal to Earth's rotation period (about 24 h), so it stays above the same point on the equator.

Multiple choice

25.For a satellite to be geostationary, it must orbit

  • Adirectly above the equator, from west to east
  • Bdirectly above one of the poles
  • Cin any plane, provided its period is 24 hours
  • Dfrom east to west above the equator

Answer: A

A geostationary orbit must lie in the equatorial plane and move west-to-east (same sense as Earth's spin) to stay fixed above one point on the equator.

Multiple choice

26.The approximate altitude of a geostationary satellite above the Earth's surface is

  • A20,000 km
  • B36,000 km
  • C400 km
  • D1,000 km

Answer: B

Using T = 24 h and Kepler's third law with Earth's GM, the orbital radius from Earth's centre is about 42,300 km, an altitude of about 36,000 km above the surface.

Multiple choice

27.Geostationary satellites are especially useful for

  • Atelecommunications and TV broadcasting, since a receiving dish can stay pointed at a fixed direction
  • Bstudying the Sun's core
  • Cmapping the Earth's poles in detail
  • Dclose-up imaging of small surface features, since they orbit very low

Answer: A

Because they appear fixed in the sky, ground antennas do not need to track them, making them ideal for continuous communication and broadcasting links.

Fill in the blank

28.A satellite that passes over (or near) both of the Earth's poles on each orbit is called a ______ satellite.

Answer: polar

Polar satellites have orbital planes that pass near the poles, allowing them to scan the whole Earth's surface as it rotates beneath them.

Multiple choice

29.Given Earth's mass M = 6.0 × 10²⁴ kg and G = 6.67 × 10⁻¹¹ N·m²/kg², estimate the orbital speed of a satellite at r = 7.0 × 10⁶ m.

  • A≈ 7.6 × 10³ m/s
  • B≈ 1.1 × 10⁴ m/s
  • C≈ 3.8 × 10³ m/s
  • D≈ 9.8 × 10² m/s

Answer: A

v = √(GM/r) = √((6.67×10⁻¹¹ × 6.0×10²⁴)/7.0×10⁶) = √(5.72×10⁷) ≈ 7.6×10³ m/s.

Multiple choice

30.Two satellites A and B orbit the Earth with radii rA and rB = 4rA. According to Kepler's third law, the ratio of their periods TB/TA is

  • A16
  • B2
  • C8
  • D4

Answer: C

T² ∝ r³, so TB/TA = (rB/rA)^(3/2) = 4^(3/2) = 8.

Multiple choice

31.The escape velocity from a planet of mass M and radius R is given by

  • Av_e = 2√(GM/R)
  • Bv_e = √(2GM/R)
  • Cv_e = √(GM/2R)
  • Dv_e = √(GM/R)

Answer: B

Escape velocity is found by equating kinetic energy to the magnitude of gravitational potential energy: ½mv_e² = GMm/R, giving v_e = √(2GM/R).

True or false

32.The escape velocity from the Earth's surface does not depend on the mass of the object being launched.

Answer: True

In v_e = √(2GM/R), the mass of the escaping object cancels out, so escape velocity is the same for all objects at a given location.

Multiple choice

33.Estimate the escape velocity from Earth's surface, given M = 6.0 × 10²⁴ kg, R = 6.4 × 10⁶ m, and G = 6.67 × 10⁻¹¹ N·m²/kg².

  • A≈ 2.2 × 10⁴ m/s
  • B≈ 5.6 × 10³ m/s
  • C≈ 7.9 × 10³ m/s
  • D≈ 1.1 × 10⁴ m/s

Answer: D

v_e = √(2GM/R) = √((2×6.67×10⁻¹¹×6.0×10²⁴)/6.4×10⁶) = √(1.25×10⁸) ≈ 1.12×10⁴ m/s.

Multiple choice

34.Gravitational potential energy of a mass m at distance r from mass M is usually written as U = −GMm/r. The negative sign indicates that

  • Agravitational potential energy is taken to be zero at infinite separation and decreases (becomes more negative) as masses get closer
  • Bthe masses are moving apart
  • Cthe calculation has an error and should be positive
  • Dthe gravitational force is repulsive

Answer: A

The zero of potential energy is conventionally chosen at infinite separation; since gravity does positive work as masses approach, the potential energy becomes negative (lower) at finite separation.

Multiple choice

35.Which statement about the direction of the gravitational field of a uniform spherical mass is correct?

  • AThe field is directed tangentially around the sphere
  • BOutside the sphere, the field behaves as though all the mass were concentrated at the centre, directed radially inward
  • CThe field points radially outward from the sphere's surface
  • DThe field has no definite direction outside a sphere

Answer: B

For a uniform sphere, the external gravitational field is identical to that of a point mass at the centre, always directed toward that centre.

Fill in the blank

36.According to Newton's law of gravitation, the force between two masses acts along the line ______ the two masses.

Answer: joining (connecting)

Gravitational force is a central force, acting along the straight line joining the centres of the two masses.

Multiple choice

37.A 60 kg astronaut orbits Earth at a height where g = 8.7 m/s². Their apparent weight (as measured by a scale in the spacecraft) would read approximately

  • A588 N, their weight on Earth's surface
  • Bzero, because they are in free fall together with the spacecraft
  • C60 N
  • D522 N, the same as the gravitational force on them

Answer: B

In orbit, both astronaut and spacecraft are in free fall under gravity providing the centripetal force, so there is no normal contact force — the astronaut experiences apparent weightlessness even though gravity (≈522 N) still acts on them.

True or false

38.For two satellites orbiting the same planet, the one in the larger orbit moves with a greater orbital speed.

Answer: False

Since v = √(GM/r), orbital speed decreases as orbital radius increases; the outer satellite moves slower.

Multiple choice

39.A key assumption used to derive g = g₀(1 − d/R) for the variation of gravity with depth is that

  • Athe Earth is a perfect point mass at all depths
  • Bgravity is unaffected by the presence of mass above the point
  • Cthe Earth's density is uniform throughout its volume
  • Dthe Earth's mass is entirely concentrated at its centre

Answer: C

This simple linear model treats the Earth as a uniform-density sphere, so only the mass enclosed within radius (R − d) contributes to g at that depth.

Multiple choice

40.If Earth's mass were to suddenly double while its radius stayed the same, the surface value of g would

  • Aquadruple
  • Bhalve
  • Cstay the same
  • Ddouble

Answer: D

g = GM/R²; if M doubles and R is unchanged, g doubles proportionally.

Back to top ↑

Unit 6: Atomic Models

Multiple choice

1.Thomson's 'plum pudding' model of the atom described the atom as

  • Aa collection of neutrons and protons with no electrons at all
  • Ba sphere of uniformly distributed positive charge with electrons embedded in it, like plums in a pudding
  • Ca tiny, dense, positively charged nucleus orbited by electrons in fixed shells
  • Da cloud of negative charge with a small positive nucleus at its centre

Answer: B

Thomson pictured the atom as a uniform sphere of positive charge with negatively charged electrons distributed throughout it, resembling plums embedded in a pudding.

Multiple choice

2.The alpha-particle scattering experiment that led to Rutherford's nuclear model was performed by

  • AChadwick and Rutherford together in 1932
  • BBohr and Planck
  • CGeiger and Marsden, under Rutherford's direction
  • DThomson and Millikan

Answer: C

Geiger and Marsden fired alpha particles at thin gold foil under Rutherford's supervision; the results overturned Thomson's model.

Multiple choice

3.In the gold foil experiment, most alpha particles passed straight through the foil with little deflection. This suggested that

  • Athe atom is a solid, uniformly dense sphere
  • Bthe nucleus fills almost the whole atom
  • Cmost of the atom is empty space
  • Delectrons are heavier than alpha particles

Answer: C

Since the vast majority of alpha particles passed through undeflected, most of the volume of an atom must be empty space.

Multiple choice

4.A small fraction of alpha particles in Rutherford's experiment were deflected through very large angles, some almost straight back. This showed that

  • Athe atom contains a small, dense, positively charged nucleus
  • Balpha particles are negatively charged
  • Cthe atom has no positive charge at all
  • Delectrons are positively charged

Answer: A

Large-angle deflections required a concentrated positive charge and mass — the nucleus — since Thomson's spread-out charge model could not produce such strong repulsion.

True or false

5.Rutherford's nuclear model could not be explained by Thomson's plum pudding model.

Answer: True

The plum pudding model, with charge spread throughout the atom, predicts only small deflections and cannot account for the occasional large-angle scattering observed.

Multiple choice

6.In Rutherford's nuclear model of the atom, most of the atom's mass is concentrated in

  • Aempty space surrounding the atom
  • Ba diffuse cloud filling the whole atom
  • Ca tiny central nucleus
  • Dthe outer electron shells

Answer: C

Rutherford's model places almost all the mass and all the positive charge in a very small central nucleus.

Fill in the blank

7.In Rutherford's model, the negatively charged ______ orbit the positively charged nucleus.

Answer: electrons

Rutherford proposed that electrons orbit a small, dense, positive nucleus, similar to planets orbiting the Sun.

Multiple choice

8.A major weakness of Rutherford's classical nuclear model was that it could not explain

  • Awhy orbiting electrons do not continuously radiate energy and spiral into the nucleus
  • Bwhy atoms have any mass at all
  • Cwhy the nucleus is positively charged
  • Dwhy alpha particles are deflected by gold foil

Answer: A

Classical electromagnetism predicts that an accelerating (orbiting) charge should radiate energy continuously, causing electrons to spiral into the nucleus almost instantly — contrary to the observed stability of atoms.

Multiple choice

9.Bohr's model improved on Rutherford's model by proposing that

  • Athe nucleus is negatively charged
  • Belectrons can only occupy certain discrete, stable energy levels (orbits) without radiating energy
  • Catoms have no internal structure
  • Delectrons move in continuously changing, non-fixed orbits

Answer: B

Bohr postulated quantised, stable orbits (stationary states) in which electrons do not radiate energy, resolving the stability problem of Rutherford's model.

Multiple choice

10.According to Bohr's model, an atom emits a photon of light when

  • Athe nucleus splits into two smaller nuclei
  • Ban electron absorbs a photon and stays in the same level
  • Ctwo electrons collide within the same orbit
  • Dan electron falls from a higher energy level to a lower one

Answer: D

A photon is emitted when an electron makes a transition from a higher-energy level to a lower-energy level, with photon energy equal to the difference in energy levels.

Multiple choice

11.The energy of a photon emitted or absorbed during an electron transition between two atomic energy levels E1 and E2 is given by

  • Ahf = |E2 − E1|
  • Bhf = E1/E2
  • Chf = E1 + E2
  • Dhf = E1 × E2

Answer: A

By conservation of energy, the photon's energy hf exactly equals the magnitude of the energy difference between the two levels.

Multiple choice

12.Atomic energy levels are described as 'quantised' because

  • Aelectrons can have any continuous range of energy
  • Bonly the ground state has a defined energy
  • Cenergy levels are always equally spaced in every atom
  • Dan electron in an atom can only have certain specific, discrete energy values, not any value

Answer: D

Quantisation means only discrete energy values are allowed for a bound electron, in contrast to a classical continuous range.

Fill in the blank

13.The lowest energy level of an atom, in which it is most stable, is called the ______ state.

Answer: ground

The ground state is the lowest possible energy level an electron can occupy in an atom.

Multiple choice

14.An electron in an atom that has absorbed energy and moved to a higher energy level is said to be in a(n)

  • Aionised state only
  • Bexcited state
  • Cground state
  • Dneutral state

Answer: B

When an electron gains energy and jumps to a higher allowed level, the atom is said to be excited.

Multiple choice

15.For the hydrogen atom, the Bohr model gives the energy of level n as En = −13.6/n² eV. The energy of the electron in the n = 2 level is

  • A−1.51 eV
  • B−6.8 eV
  • C−13.6 eV
  • D−3.4 eV

Answer: D

En = −13.6/n² eV; for n = 2, E2 = −13.6/4 = −3.4 eV.

Multiple choice

16.Using En = −13.6/n² eV for hydrogen, the energy needed to ionise a hydrogen atom from its ground state (n = 1) is

  • A13.6 eV
  • B3.4 eV
  • C1.51 eV
  • D10.2 eV

Answer: A

Ionisation energy is the energy to raise the electron from n = 1 (E1 = −13.6 eV) to n = ∞ (E = 0), which equals 13.6 eV.

Multiple choice

17.A hydrogen electron falls from n = 3 (E3 = −1.51 eV) to n = 2 (E2 = −3.4 eV). The energy of the emitted photon is approximately

  • A3.4 eV
  • B1.89 eV
  • C4.91 eV
  • D1.51 eV

Answer: B

ΔE = E3 − E2 = −1.51 − (−3.4) = 1.89 eV, which is released as a photon.

Multiple choice

18.The set of spectral lines produced by hydrogen electron transitions ending at n = 1 is known as the

  • APaschen series
  • BBrackett series
  • CBalmer series
  • DLyman series

Answer: D

Transitions ending on the n = 1 (ground) level produce the Lyman series, which lies in the ultraviolet region.

Multiple choice

19.The Balmer series of hydrogen spectral lines corresponds to electron transitions that end at

  • An = 4
  • Bn = 1
  • Cn = 3
  • Dn = 2

Answer: D

The Balmer series consists of transitions from higher levels down to n = 2, and its lines lie mainly in the visible part of the spectrum.

Multiple choice

20.Which spectral series of hydrogen lies mainly in the visible region of the electromagnetic spectrum?

  • ABrackett series
  • BPaschen series
  • CBalmer series
  • DLyman series

Answer: C

The Balmer series (transitions ending at n = 2) produces lines with wavelengths in the visible range, historically the first hydrogen series discovered.

Multiple choice

21.The Paschen series of hydrogen spectral lines results from transitions ending at

  • An = 5
  • Bn = 2
  • Cn = 3
  • Dn = 1

Answer: C

The Paschen series consists of transitions from higher levels down to n = 3, and lies in the infrared region.

True or false

22.The Lyman series of hydrogen lines lies in the ultraviolet region of the spectrum, while the Paschen series lies in the infrared.

Answer: True

Larger energy transitions (ending at n = 1, Lyman) give higher-frequency UV photons, while smaller energy transitions (ending at n = 3, Paschen) give lower-frequency infrared photons.

Fill in the blank

23.The existence of discrete spectral lines in atomic spectra is direct evidence that atomic energy levels are ______ rather than continuous.

Answer: quantised (discrete)

Since only specific photon energies (and hence specific line wavelengths) are observed, the underlying energy levels must be discrete/quantised.

Multiple choice

24.The Rydberg formula for hydrogen spectral lines is 1/λ = R(1/n1² − 1/n2²). The Rydberg constant R has an approximate value of

  • A6.63 × 10⁻³⁴ m⁻¹
  • B1.097 × 10⁷ m⁻¹
  • C9.11 × 10⁻³¹ m⁻¹
  • D3.00 × 10⁸ m⁻¹

Answer: B

The Rydberg constant is approximately R = 1.097 × 10⁷ m⁻¹, used to calculate hydrogen spectral line wavelengths.

Multiple choice

25.Emission line spectra are produced when

  • Aa solid is heated until it becomes a continuous glowing spectrum
  • Bwhite light passes through a cool gas and certain wavelengths are absorbed
  • Celectrons are permanently removed from all atoms in a sample
  • Dexcited atoms of a gas emit photons as electrons fall to lower energy levels

Answer: D

An emission spectrum consists of discrete bright lines produced when electrons in excited atoms fall to lower energy levels, releasing photons of specific energies.

Multiple choice

26.Absorption spectra appear as

  • Arandomly scattered bright and dark patches with no pattern
  • Bdark lines at specific wavelengths against an otherwise continuous bright background spectrum
  • Ca smooth, unbroken rainbow of colour with no lines
  • Dbright lines on a completely dark background

Answer: B

When continuous-spectrum light passes through a cooler gas, atoms absorb photons matching their energy-level differences, producing dark lines in the transmitted spectrum at those exact wavelengths.

Multiple choice

27.One important application of atomic spectral analysis is

  • Aproducing sound waves for communication
  • Bidentifying the chemical elements present in stars from their spectral lines
  • Cgenerating nuclear fusion reactions in the laboratory
  • Dmeasuring the mass of the Earth directly

Answer: B

Each element has a unique set of spectral lines (a 'fingerprint'), allowing astronomers to identify elements present in stars and other distant sources through spectroscopy.

Multiple choice

28.Thermionic emission is the process by which

  • Aelectrons are emitted from the surface of a heated metal when they gain enough energy to overcome the work function
  • Belectrons are emitted from a metal due to a strong externally applied electric field alone at room temperature
  • Celectrons are knocked out of a metal surface by incident light photons
  • Dprotons are released from the nucleus of an atom

Answer: A

Thermionic emission occurs when heating a metal (usually a filament) gives free electrons enough kinetic energy to escape the surface, overcoming the work function.

Multiple choice

29.The work function of a metal is defined as

  • Athe minimum energy needed to remove an electron from the surface of the metal
  • Bthe total energy of all free electrons in the metal
  • Cthe energy released when an electron enters the metal
  • Dthe electrical resistance of the metal surface

Answer: A

Work function φ is the minimum energy required to liberate an electron from a metal's surface into the surrounding vacuum.

Multiple choice

30.Which of the following factors increases the rate of thermionic emission from a metal filament?

  • AUsing a metal with a very high melting point but keeping temperature the same
  • BIncreasing the work function of the metal
  • CDecreasing the temperature of the filament
  • DIncreasing the temperature of the filament

Answer: D

Thermionic emission increases strongly with temperature, since more electrons gain enough thermal energy to exceed the work function as temperature rises.

Multiple choice

31.A metal with a lower work function will, at the same temperature, generally show

  • Aa higher rate of thermionic emission
  • Bthe same emission rate as any other metal
  • Cno thermionic emission at all
  • Da lower rate of thermionic emission

Answer: A

A lower work function means less energy is needed for electrons to escape, so more electrons are emitted at a given temperature.

Multiple choice

32.Which of the following is NOT typically listed as a factor affecting the rate of thermionic emission?

  • AThe surface area of the emitting filament
  • BThe work function (material) of the emitting surface
  • CThe colour of light shining on the filament
  • DThe temperature of the filament

Answer: C

Thermionic emission depends on temperature, work function, and emitting surface area/condition; it is a thermal process and does not depend on the colour of any incident light (that describes the photoelectric effect instead).

True or false

33.Increasing the surface area of a heated filament, while keeping temperature and material constant, increases the total thermionic emission current.

Answer: True

A larger emitting area provides more electrons at the surface with sufficient energy to escape, increasing the overall emission current at a given temperature.

Fill in the blank

34.In a vacuum tube, the heated component that emits electrons by thermionic emission is called the ______.

Answer: cathode (filament/heater)

The cathode (often a heated filament) is the electrode from which electrons are thermionically emitted in devices such as vacuum tubes and cathode ray tubes.

Multiple choice

35.An applied electric field near a heated metal surface can increase thermionic emission by

  • Areversing the charge of emitted electrons
  • Blowering the effective potential barrier at the surface (the Schottky effect), helping electrons escape
  • Chaving no effect whatsoever on emission
  • Dcooling the metal surface

Answer: B

A strong external electric field at the surface reduces the effective work function barrier, an effect known as the Schottky effect, enhancing thermionic emission.

True or false

36.Thomson's model correctly predicted the existence of a small, dense, positively charged nucleus at the centre of the atom.

Answer: False

Thomson's plum pudding model had positive charge spread throughout the whole atom; the concentrated nucleus was proposed later by Rutherford.

Multiple choice

37.Bohr's model successfully explained the line spectrum of which atom, matching experimental spectral line wavelengths closely?

  • AUranium
  • BHelium
  • CHydrogen
  • DIron

Answer: C

Bohr's model gives an accurate quantitative account of the hydrogen atom's spectral lines, though it becomes far less accurate for multi-electron atoms.

Multiple choice

38.A vacuum diode uses thermionic emission from a heated cathode; the emitted electrons are then accelerated toward the

  • Aanode, which is held at a higher (positive) potential
  • Bouter glass envelope of the tube
  • Ccathode itself
  • Dgrid, which is always negative

Answer: A

Electrons emitted from the heated cathode are attracted to and collected by the positively charged anode, producing current flow through the tube.

Fill in the blank

39.The energy required to completely remove an electron from an atom, taking it from its ground state to infinity, is called the ______ energy.

Answer: ionisation

Ionisation energy is the minimum energy needed to free a ground-state electron completely from the atom, corresponding to a transition from n = 1 to n = ∞.

Multiple choice

40.Compared to Rutherford's classical model, Bohr's key new assumption was that

  • Aelectrons have no mass
  • Bthe nucleus is negatively charged
  • Cangular momentum of an orbiting electron is quantised in integer multiples of h/2π
  • Dall electrons occupy exactly the same energy level

Answer: C

Bohr postulated that electron angular momentum is quantised, L = nh/2π (n = 1, 2, 3, ...), which restricts electrons to specific allowed orbits/energy levels.

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Unit 7: Wave and Particle Nature of Light

Multiple choice

1.A blackbody is best described as an object that

  • Aemits only radiation in the visible spectrum
  • Breflects all radiation incident on it perfectly
  • Cis coloured completely black and never emits any radiation
  • Dabsorbs all electromagnetic radiation incident on it, at every wavelength

Answer: D

An ideal blackbody absorbs all incident radiation (reflecting none) and is also the most efficient possible emitter of thermal radiation at every wavelength.

Multiple choice

2.The Stefan-Boltzmann law for the total power radiated by a blackbody is given by

  • AP = σA/T⁴
  • BP = σAT
  • CP = σAT⁴
  • DP = σAT²

Answer: C

The Stefan-Boltzmann law states P = σAT⁴, where σ is the Stefan-Boltzmann constant, A is surface area, and T is absolute temperature.

Fill in the blank

3.In the Stefan-Boltzmann law P = σAT⁴, the symbol σ represents the ______ constant, with value approximately 5.67 × 10⁻⁸ W m⁻² K⁻⁴.

Answer: Stefan-Boltzmann

σ (sigma) is the Stefan-Boltzmann constant, σ ≈ 5.67 × 10⁻⁸ W/(m²K⁴).

Multiple choice

4.A blackbody of surface area 0.02 m² is at an absolute temperature of 500 K. Using σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴, its radiated power is approximately

  • A709 W
  • B7.09 W
  • C0.709 W
  • D70.9 W

Answer: D

P = σAT⁴ = 5.67×10⁻⁸ × 0.02 × (500)⁴ = 5.67×10⁻⁸ × 0.02 × 6.25×10¹⁰ ≈ 70.9 W.

True or false

5.According to the Stefan-Boltzmann law, if the absolute temperature of a blackbody doubles, the power it radiates increases by a factor of 16.

Answer: True

Since P ∝ T⁴, doubling T multiplies power by 2⁴ = 16.

Multiple choice

6.The classical (Rayleigh-Jeans) theory of blackbody radiation failed at short wavelengths, a problem historically known as the

  • Ainfrared collapse
  • Bquantum tunnelling problem
  • Cultraviolet catastrophe
  • Dphotoelectric paradox

Answer: C

Classical wave theory predicted infinite radiated energy at short (ultraviolet) wavelengths, a clear contradiction with experiment called the ultraviolet catastrophe.

Multiple choice

7.Planck resolved the ultraviolet catastrophe by proposing that

  • Alight travels only as a continuous wave with no minimum energy unit
  • Belectromagnetic energy is emitted or absorbed only in discrete packets (quanta) of energy E = hf
  • Cblackbodies do not actually emit radiation
  • Dthe speed of light varies with frequency

Answer: B

Planck's quantum hypothesis assumed oscillators in the blackbody could only have energies that are integer multiples of hf, successfully matching the observed spectrum.

Multiple choice

8.In Planck's quantum theory, the energy of one quantum of radiation of frequency f is given by

  • AE = h/f
  • BE = hf
  • CE = hf²
  • DE = h²f

Answer: B

Planck proposed that radiant energy is quantised in units of E = hf, where h is Planck's constant.

Fill in the blank

9.Planck's constant h has an approximate value of ______ J·s.

Answer: 6.63 × 10⁻³⁴

Planck's constant is h ≈ 6.63 × 10⁻³⁴ J s, relating a photon's energy to its frequency via E = hf.

Multiple choice

10.According to the photon theory of light, a beam of light can be thought of as consisting of

  • Asound-like pressure waves travelling through the ether
  • Bonly a classical electromagnetic wave with no particle behaviour
  • Cdiscrete packets of energy called photons, each carrying energy E = hf
  • Da continuous stream of massive particles with no wave properties

Answer: C

Einstein's photon theory treats light as a stream of discrete energy quanta (photons), each with energy E = hf.

Multiple choice

11.Calculate the energy of a photon of light with frequency 6.0 × 10¹⁴ Hz, given h = 6.63 × 10⁻³⁴ J·s.

  • A3.98 × 10⁻¹⁵ J
  • B3.98 × 10⁻¹⁹ J
  • C6.63 × 10⁻³⁴ J
  • D1.10 × 10⁻⁴⁸ J

Answer: B

E = hf = 6.63×10⁻³⁴ × 6.0×10¹⁴ = 3.98×10⁻¹⁹ J.

Multiple choice

12.The energy of a photon can also be written in terms of wavelength λ and the speed of light c as

  • AE = hc/λ
  • BE = hλ/c
  • CE = hcλ
  • DE = h/(cλ)

Answer: A

Since c = fλ, substituting f = c/λ into E = hf gives E = hc/λ.

Multiple choice

13.A photon has a wavelength of 500 nm. Using h = 6.63 × 10⁻³⁴ J·s and c = 3.0 × 10⁸ m/s, its energy is approximately

  • A1.99 × 10⁻²⁵ J
  • B6.63 × 10⁻¹⁹ J
  • C3.98 × 10⁻¹⁶ J
  • D3.98 × 10⁻¹⁹ J

Answer: D

E = hc/λ = (6.63×10⁻³⁴ × 3.0×10⁸)/(500×10⁻⁹) = (1.989×10⁻²⁵)/(5×10⁻⁷) ≈ 3.98×10⁻¹⁹ J.

Multiple choice

14.Wave-particle duality refers to the idea that

  • Aonly matter, not light, can show wave and particle behaviour
  • Blight is always a wave and never behaves like a particle
  • Clight is always made of particles and never behaves like a wave
  • Dlight (and matter) can exhibit both wave-like and particle-like properties, depending on the experiment

Answer: D

Wave-particle duality states that light and matter both display wave behaviour (interference, diffraction) and particle behaviour (photons, quantised energy), depending on how they are observed.

Multiple choice

15.The principle of complementarity, introduced by Bohr, states that

  • Athe wave and particle aspects of light are complementary; a single experiment can reveal one aspect at a time but never both simultaneously
  • Blight behaves only as a wave under all experimental conditions
  • Cwave and particle models of light are entirely incompatible and one must be discarded
  • Dparticles have no associated wave properties at all

Answer: A

Complementarity holds that wave and particle descriptions are both necessary and complementary, but a given experimental setup will reveal only one aspect at a time.

True or false

16.Interference and diffraction experiments demonstrate the wave nature of light, while the photoelectric effect demonstrates its particle nature.

Answer: True

Interference/diffraction patterns arise from superposition of waves, whereas the photoelectric effect is best explained by treating light as discrete photons.

Multiple choice

17.In the photoelectric effect, the threshold frequency is defined as

  • Athe frequency at which the maximum number of photoelectrons is emitted
  • Bthe frequency corresponding to red light in every metal
  • Cthe minimum frequency of incident light below which no photoelectrons are emitted, regardless of intensity
  • Dthe frequency of light that gives photoelectrons the least possible kinetic energy

Answer: C

Threshold frequency f₀ is the minimum frequency needed so that a single photon has enough energy to overcome the work function; below f₀, no photoemission occurs no matter how intense the light.

Multiple choice

18.Einstein's photoelectric equation is written as

  • Ahf = φ × KE_max
  • Bhf = φ + KE_max
  • Chf = φ − KE_max
  • Dhf = φ/KE_max

Answer: B

Energy conservation gives the photon energy hf equal to the work function φ plus the maximum kinetic energy KE_max of the emitted electron.

Multiple choice

19.The work function of a metal in the photoelectric effect is

  • Athe frequency of the incident light
  • Bthe minimum energy needed to eject an electron from the metal's surface
  • Cthe stopping potential of the photocell
  • Dthe total kinetic energy of all electrons ejected from the metal

Answer: B

The work function φ represents the minimum energy an electron must gain to escape the metal surface.

Multiple choice

20.In a photoelectric experiment, the stopping potential is the

  • Areverse voltage needed to just stop the most energetic photoelectrons from reaching the collector
  • Bpotential difference across the light source
  • Cvoltage that produces the maximum photoelectric current
  • Dvoltage that increases the frequency of the incident light

Answer: A

The stopping potential V₀ is the minimum reverse voltage required to bring the photocurrent to zero, related to maximum kinetic energy by eV₀ = KE_max.

Multiple choice

21.A metal has a work function of 2.0 eV. Light of frequency 1.0 × 10¹⁵ Hz (energy ≈ 4.14 eV) is shone on it. The maximum kinetic energy of emitted photoelectrons is approximately

  • A2.14 eV
  • B2.0 eV
  • C4.14 eV
  • D6.14 eV

Answer: A

KE_max = hf − φ = 4.14 eV − 2.0 eV = 2.14 eV.

Multiple choice

22.In the photoelectric effect, increasing the intensity of light (above the threshold frequency) while keeping frequency constant results in

  • Afewer photoelectrons emitted per second
  • Bmore photoelectrons emitted per second, but the same maximum kinetic energy per electron
  • Ca higher maximum kinetic energy for each photoelectron
  • Dno photoelectrons at all, regardless of frequency

Answer: B

Intensity controls the number of photons per second, hence the number of photoelectrons emitted, but each photon still carries the same energy hf, so maximum kinetic energy is unchanged.

True or false

23.According to Einstein's photoelectric theory, the maximum kinetic energy of photoelectrons increases with the frequency of incident light, not its intensity.

Answer: True

KE_max = hf − φ depends only on frequency (via hf) and the work function, not on light intensity, which affects only the number of photoelectrons.

Multiple choice

24.If the frequency of incident light on a metal surface is below the threshold frequency, then

  • Ano photoelectrons are emitted no matter how intense the light is
  • Bthe metal emits electrons continuously regardless of frequency
  • Cphotoelectrons are emitted but with zero kinetic energy
  • Dphotoelectrons are emitted only if the light is very intense

Answer: A

Below threshold frequency, individual photons do not carry enough energy to overcome the work function, so no photoelectrons are emitted regardless of intensity.

Fill in the blank

25.The stopping potential V₀ is related to the maximum kinetic energy of photoelectrons by the equation KE_max = ______.

Answer: eV₀

The work done against the stopping (retarding) potential equals the maximum kinetic energy: eV₀ = KE_max, where e is the electron's charge.

Multiple choice

26.A photocell has a threshold wavelength of 600 nm. Using hc ≈ 1240 eV·nm, the work function of the metal is approximately

  • A0.60 eV
  • B1.24 eV
  • C3.10 eV
  • D2.07 eV

Answer: D

φ = hc/λ₀ = 1240 eV·nm / 600 nm ≈ 2.07 eV.

Multiple choice

27.The photoelectric effect provided strong evidence for the

  • Apurely wave nature of light
  • Bidea that light has no energy at all
  • Cexistence of the ether
  • Dparticle (photon) nature of light

Answer: D

Classical wave theory could not explain the instantaneous emission, threshold frequency, or intensity-independence of kinetic energy seen in the photoelectric effect; Einstein's photon model explained all of these.

Multiple choice

28.When a photon collides with a free electron and transfers some energy and momentum to it, causing the scattered photon to have a longer wavelength, this phenomenon is called

  • Athe photoelectric effect
  • Bthe Compton effect
  • Cthermionic emission
  • Dthe Doppler effect

Answer: B

In Compton scattering, a photon transfers part of its energy and momentum to an electron, resulting in a scattered photon of lower energy (longer wavelength) — direct evidence of photon momentum.

Multiple choice

29.de Broglie proposed that particles of matter, such as electrons, have an associated wavelength given by

  • Aλ = h/p (where p is the particle's momentum)
  • Bλ = pE/h
  • Cλ = hp
  • Dλ = h/E

Answer: A

The de Broglie wavelength relates a particle's wave nature to its momentum: λ = h/p = h/(mv).

Multiple choice

30.An electron of mass 9.11 × 10⁻³¹ kg moves at 2.0 × 10⁶ m/s. Using h = 6.63 × 10⁻³⁴ J·s, its de Broglie wavelength is approximately

  • A3.6 × 10⁻⁷ m
  • B7.3 × 10⁻¹⁰ m
  • C3.6 × 10⁻¹⁰ m
  • D1.8 × 10⁻¹⁰ m

Answer: C

λ = h/(mv) = 6.63×10⁻³⁴/(9.11×10⁻³¹ × 2.0×10⁶) = 6.63×10⁻³⁴/1.822×10⁻²⁴ ≈ 3.6×10⁻¹⁰ m.

True or false

31.The wave nature of matter, proposed by de Broglie, has been experimentally confirmed by electron diffraction experiments.

Answer: True

Davisson and Germer's electron diffraction experiment showed electrons producing diffraction patterns, confirming their wave-like behaviour as predicted by de Broglie.

Multiple choice

32.Because de Broglie's wavelength λ = h/p is inversely proportional to momentum, macroscopic (large, everyday) objects have de Broglie wavelengths that are

  • Aextremely small and undetectable, so their wave nature is not observed in daily life
  • Bextremely large, easily observed as diffraction in daily life
  • Calways equal to the wavelength of visible light
  • Dexactly equal to their physical size

Answer: A

Since ordinary objects have large momentum, h/p becomes vanishingly small, far too tiny to produce observable wave effects, unlike for electrons or other subatomic particles.

Multiple choice

33.Which observation is best explained using the particle (photon) model of light rather than the wave model?

  • ADiffraction of light around obstacles
  • BThe formation of interference fringes in Young's double-slit experiment
  • CPolarisation of light
  • DThe existence of a sharp threshold frequency in the photoelectric effect

Answer: D

A threshold frequency, below which no photoemission occurs regardless of intensity, is naturally explained only if light energy comes in discrete photon packets of energy hf.

Fill in the blank

34.The energy carried by a single photon of electromagnetic radiation is directly proportional to its ______.

Answer: frequency

From E = hf, photon energy is directly proportional to the frequency of the radiation (and inversely proportional to its wavelength).

Multiple choice

35.As the temperature of a blackbody increases, the wavelength at which it emits most strongly (according to Wien's displacement law)

  • Astays exactly the same
  • Bincreases (shifts toward longer wavelengths)
  • Cdecreases (shifts toward shorter wavelengths)
  • Dbecomes infinite

Answer: C

Wien's displacement law, λ_max T = constant, shows that as temperature increases, the peak emission wavelength shifts to shorter (bluer) wavelengths.

Multiple choice

36.A star's surface radiates approximately as a blackbody. If Star A has twice the absolute surface temperature of Star B but the same surface area, Star A radiates power that is

  • A8 times that of Star B
  • B2 times that of Star B
  • C16 times that of Star B
  • D4 times that of Star B

Answer: C

P ∝ T⁴, so doubling T multiplies radiated power by 2⁴ = 16, assuming equal surface areas.

Multiple choice

37.Which of the following best explains why increasing the intensity of light below the threshold frequency still produces no photoelectrons?

  • AHigher intensity light has fewer photons
  • BElectrons absorb energy over long times until enough builds up, regardless of frequency
  • CIncreasing intensity always increases photon frequency
  • DEach photon still carries insufficient energy (hf < φ), and electrons cannot combine energy from multiple photons

Answer: D

In the photon model, each photoelectron interacts with (and absorbs) essentially one photon at a time; if a single photon's energy hf is below φ, emission cannot occur, however many such photons arrive.

Multiple choice

38.The graph of maximum kinetic energy of photoelectrons (KE_max) versus frequency (f) of incident light is a straight line whose gradient represents

  • Athe speed of light, c
  • Bthe work function, φ
  • CPlanck's constant, h
  • Dthe stopping potential, V₀

Answer: C

Rearranging Einstein's equation gives KE_max = hf − φ, a straight line of the form y = mx + c with gradient h and y-intercept −φ.

Multiple choice

39.In the KE_max versus frequency graph for the photoelectric effect, the frequency-axis intercept represents

  • Athe work function, φ, directly in joules
  • Bthe threshold frequency, f₀
  • Cthe stopping potential
  • DPlanck's constant

Answer: B

The line KE_max = hf − φ crosses the frequency axis (KE_max = 0) at f = φ/h, which is the threshold frequency f₀.

Multiple choice

40.Complementarity in quantum physics is closely linked to which idea?

  • AThat no single experiment can simultaneously display both the fully wave-like and fully particle-like nature of light
  • BThat measurement never affects a quantum system
  • CThat light always behaves identically to sound waves
  • DThat classical physics fully explains all quantum phenomena

Answer: A

Complementarity states that wave and particle descriptions apply under different experimental conditions, and a single measurement setup reveals only one of these aspects at a time.

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Unit 8: Signals and Communication Systems

Multiple choice

1.Communication, in the context of physics and engineering, is best defined as

  • Athe process of generating electricity from mechanical energy
  • Bthe conversion of heat into mechanical work
  • Cthe storage of information in a computer memory
  • Dthe process of transferring information from one point (sender) to another (receiver) using a signal

Answer: D

Communication is the transfer of information from a transmitting point to a receiving point via some form of signal carried through a channel.

Multiple choice

2.Why is communication important in modern society?

  • AIt replaces the need for transportation entirely
  • BIt allows rapid, reliable sharing of information over long distances for business, education, safety and social connection
  • CIt has no real practical importance beyond entertainment
  • DIt only matters for military applications

Answer: B

Effective communication systems enable fast exchange of information essential for business, education, emergency services, governance and everyday social life.

Multiple choice

3.Which of the following is an example of a wired (guided) communication system?

  • ASatellite communication
  • BTelephone communication over copper cables or optical fibre
  • CRadio broadcasting through the atmosphere
  • DMobile phone communication via cell towers

Answer: B

Wired systems use a physical medium such as copper cable or optical fibre to guide the signal, unlike radio, satellite or mobile systems which use free-space electromagnetic waves.

Multiple choice

4.Which of the following is an example of a wireless communication system?

  • ARadio broadcasting
  • BLandline telephone using copper wire
  • CFibre-optic internet cable
  • DCoaxial cable television

Answer: A

Radio broadcasting transmits electromagnetic waves through free space (air) rather than along a physical conductor, making it a wireless system.

Multiple choice

5.The three basic components shown in the block diagram of a general communication system are

  • Amodulator, demodulator, and filter only
  • Bmicrophone, amplifier, and loudspeaker
  • Cantenna, battery, and switch
  • Dtransmitter, channel, and receiver

Answer: D

Every communication system can be represented in block form as: information source → transmitter → channel (medium) → receiver → destination.

Multiple choice

6.In a communication system, the function of the transmitter is to

  • Aprocess and convert the input information signal into a form suitable for transmission through the channel
  • Bstore information indefinitely without transmitting it
  • Calways convert digital data into printed text
  • Dreceive and decode the final message for the user

Answer: A

The transmitter takes the original message signal and processes it (e.g. amplifies, modulates) so that it can be efficiently sent through the communication channel.

Multiple choice

7.The channel in a communication system refers to

  • Athe physical medium through which the signal travels from transmitter to receiver
  • Bthe component that displays the final received message
  • Cthe battery that powers the transmitter
  • Dthe device that generates the original message

Answer: A

The channel is the medium — such as a cable, optical fibre, or free space — that carries the signal from the transmitter to the receiver.

Multiple choice

8.The function of the receiver in a communication system is to

  • Aalways encrypt the message further before delivery
  • Bgenerate the original information signal
  • Cpick up the transmitted signal from the channel and convert it back into a usable form of the original information
  • Damplify only the transmitter's power supply

Answer: C

The receiver detects the incoming signal and processes it (e.g. demodulates, amplifies) to reconstruct the original information for the destination.

Fill in the blank

9.In a block diagram of a communication system, information travels in the order: information source → ______ → channel → receiver → destination.

Answer: transmitter

The standard block diagram places the transmitter between the information source and the channel, converting the message for transmission.

True or false

10.Noise is an unwanted disturbance that can be introduced into a signal as it passes through the communication channel.

Answer: True

Noise refers to random, unwanted signals that interfere with and can degrade the quality of the transmitted information as it travels through the channel.

Multiple choice

11.A signal, in communication systems, is defined as

  • Aa fixed constant value with no variation over time
  • Ba physical quantity (such as voltage or current) that varies with time and carries information
  • Cany object used to build a transmitter
  • Dthe noise present in a communication channel

Answer: B

A signal is a time-varying physical quantity, typically an electrical voltage or current, used to represent and carry information.

Multiple choice

12.An analogue signal is one that

  • Acan only take one of two discrete values, 0 or 1
  • Bis always transmitted using light instead of electricity
  • Cvaries continuously in amplitude and time, taking any value within a range
  • Dnever carries any information

Answer: C

An analogue signal is continuous, capable of taking any value over a range, in contrast to a digital signal which is restricted to discrete levels.

Multiple choice

13.A digital signal is one that

  • Atakes only discrete (usually two) distinct values, typically represented as 0s and 1s
  • Balways has a sinusoidal waveform
  • Cvaries smoothly and continuously with time
  • Dcannot be processed by computers

Answer: A

Digital signals are represented using discrete levels, most commonly binary values of 0 and 1, unlike the continuously varying analogue signal.

True or false

14.Digital signals are generally more resistant to noise than analogue signals, since small variations can often still be correctly interpreted as one of the discrete levels.

Answer: True

Because digital signals only need to be distinguished between a small number of discrete levels, minor noise-induced distortions are less likely to cause misinterpretation compared with continuous analogue signals.

Multiple choice

15.Which of the following is an example of an analogue signal?

  • AA sequence of 0s and 1s stored in memory
  • BA binary computer data stream
  • CThe output voltage of a microphone directly picking up sound
  • DA digital clock display signal

Answer: C

A microphone converts continuously varying sound pressure into a continuously varying voltage, which is an analogue signal.

Multiple choice

16.The process of converting a digital signal into an analogue signal is called

  • AAnalog-to-Digital Conversion (ADC)
  • BDigital-to-Analogue Conversion (DAC)
  • Cmodulation only
  • Damplification

Answer: B

A Digital-to-Analogue Converter (DAC) transforms discrete digital data back into a continuously varying analogue signal, for example to drive a loudspeaker.

Multiple choice

17.The process of converting an analogue signal into a digital signal is called

  • Ademodulation
  • BDigital-to-Analogue Conversion (DAC)
  • Crectification
  • DAnalog-to-Digital Conversion (ADC)

Answer: D

An Analog-to-Digital Converter (ADC) samples a continuous analogue signal and represents it as discrete digital values.

Fill in the blank

18.A device that converts an analogue signal into a digital signal is called a(n) ______.

Answer: ADC (Analog-to-Digital Converter)

An ADC samples and quantises a continuous analogue signal into discrete digital values for processing, storage or transmission.

Multiple choice

19.Why is signal conversion (ADC/DAC) important in modern communication systems?

  • AIt permanently destroys the original information
  • BIt has no practical use in real systems
  • CIt allows digital processing, storage and long-distance transmission of signals that originate as, or must be delivered as, analogue quantities
  • DIt only matters for military communication

Answer: C

Signal conversion lets real-world analogue signals (like sound) be processed digitally for benefits such as noise resistance, easy storage and compression, then converted back to analogue for output (e.g. sound from a speaker).

True or false

20.A CD or digital audio player must use a Digital-to-Analogue Converter (DAC) to convert stored digital audio data back into an analogue signal that a loudspeaker can reproduce as sound.

Answer: True

Digital audio is stored as binary data; a DAC reconstructs this into a continuously varying analogue voltage signal that drives the speaker.

Multiple choice

21.Modulation, in communication systems, is defined as

  • Athe conversion of a digital signal into binary code
  • Bthe process of amplifying a signal without changing any of its properties
  • Cthe complete removal of noise from a channel
  • Dthe process of varying a property (amplitude, frequency, or phase) of a high-frequency carrier wave in accordance with the information signal

Answer: D

Modulation impresses the information signal onto a high-frequency carrier wave by varying one of the carrier's characteristics (amplitude, frequency, or phase).

Multiple choice

22.The main reason a message (baseband) signal is modulated onto a high-frequency carrier before transmission is to

  • Aconvert the signal permanently into a digital format
  • Bincrease the noise in the channel deliberately
  • Cmake the signal completely silent
  • Dallow efficient transmission over long distances using practically sized antennas, and to enable multiple signals to share the spectrum

Answer: D

Low-frequency baseband signals would require impractically large antennas and cannot easily share a transmission medium; modulating onto a high-frequency carrier solves both problems by enabling practical antenna sizes and frequency-division of channels.

Multiple choice

23.In Amplitude Modulation (AM), the property of the carrier wave that is varied according to the information signal is its

  • Aphase
  • Bamplitude
  • Cwavelength only
  • Dfrequency

Answer: B

In AM, the carrier's amplitude is made to vary in step with the instantaneous amplitude of the message signal, while its frequency stays constant.

Multiple choice

24.In Frequency Modulation (FM), the property of the carrier wave that is varied according to the information signal is its

  • ADC offset only
  • Bfrequency
  • Cwavelength of the message signal
  • Damplitude

Answer: B

In FM, the carrier's frequency is varied in proportion to the instantaneous amplitude of the message signal, while the carrier's amplitude remains constant.

True or false

25.FM (Frequency Modulation) broadcasting is generally less affected by amplitude-based noise and static than AM (Amplitude Modulation) broadcasting.

Answer: True

Since information in FM is carried in frequency variations rather than amplitude variations, amplitude-based noise (such as electrical interference) has much less effect on FM signal quality than on AM.

Multiple choice

26.Which type of modulation keeps the carrier wave's frequency constant but changes its amplitude to match the message signal?

  • APhase Modulation (PM)
  • BPulse Code Modulation only
  • CFrequency Modulation (FM)
  • DAmplitude Modulation (AM)

Answer: D

AM varies carrier amplitude while frequency stays fixed; this is the defining feature that distinguishes it from FM and PM.

Fill in the blank

27.The high-frequency wave onto which an information signal is impressed during modulation is called the ______ wave.

Answer: carrier

The carrier wave is the high-frequency signal that 'carries' the lower-frequency information signal after modulation.

Multiple choice

28.A radio communication system fundamentally consists of

  • Aa keyboard and a computer monitor
  • Ba single antenna with no transmitter or receiver
  • Ca transmitter with antenna, a transmission channel (free space), and a receiver with antenna
  • Donly a microphone and a loudspeaker connected directly by wire

Answer: C

A basic radio communication system has a transmitting station (with modulator and antenna), free space as the channel, and a receiving station (with antenna, demodulator, and output device).

Multiple choice

29.In a radio receiver, the component that extracts the original information signal from the modulated carrier wave is called the

  • Amodulator
  • Boscillator only
  • Cdemodulator (detector)
  • Dpower amplifier only

Answer: C

The demodulator (or detector) reverses the modulation process at the receiver, recovering the original message signal from the received modulated carrier.

Multiple choice

30.The antenna in a radio communication system is used to

  • Aradiate electromagnetic waves into space (transmitting antenna) or intercept them from space (receiving antenna)
  • Bstore electrical energy permanently
  • Camplify audio signals only
  • Dconvert sound directly into digital code

Answer: A

An antenna converts electrical signals into radiated electromagnetic waves for transmission, or captures incoming electromagnetic waves and converts them back into electrical signals for reception.

True or false

31.In early telecommunication history, Post, Telegraph and Telephone (PTT) organisations were often the state bodies responsible for postal services as well as telegraph and telephone networks.

Answer: True

Historically, many countries had a single government-run PTT authority that managed postal delivery alongside telegraph and telephone communication services before these were later separated or privatised.

Multiple choice

32.The telegraph, an early form of long-distance electrical communication, primarily transmitted messages using

  • Acoded electrical pulses (such as Morse code) sent along wires
  • Bcontinuous analogue voice signals
  • Cdigital packets over the internet
  • Dmodulated radio waves through free space only

Answer: A

The electrical telegraph sent messages as a series of on/off electrical pulses, commonly encoded using Morse code, along a wire connection between stations.

Multiple choice

33.Compared to the telegraph, the telephone represented an advance because it allowed

  • Adirect transmission of the human voice as a continuously varying (analogue) electrical signal
  • Bthe elimination of all wires in communication
  • Ctransmission of only written text messages
  • Dcommunication only within a single building

Answer: A

The telephone converts sound (voice) directly into a varying electrical signal that can be transmitted and reconverted into sound, unlike the telegraph which sent coded pulses representing letters.

Multiple choice

34.A key advantage of digital communication systems over analogue systems is that digital signals

  • Aare never affected by any interference at all
  • Balways require less bandwidth than analogue signals
  • Ccan be regenerated (cleaned up) at intervals along long transmission paths, reducing the buildup of noise
  • Dcannot be stored or processed by computers

Answer: C

Digital signals, being discrete, can be detected and regenerated cleanly at repeater stations, preventing the accumulation of noise that occurs in analogue systems over long distances.

Multiple choice

35.Which of the following is an example of a modern digital communication system?

  • AThe original 19th century electrical telegraph
  • BMobile (cellular) telephone networks using digital voice and data encoding
  • CAn analogue vinyl record player
  • DTraditional analogue AM radio broadcasting

Answer: B

Modern mobile networks convert voice and data into digital form for transmission, offering better noise resistance, security and efficient use of bandwidth.

Fill in the blank

36.A device that converts sound waves into an electrical signal for transmission, such as in a telephone or radio microphone, is called a ______.

Answer: microphone (transducer)

A microphone is a transducer that converts acoustic (sound) energy into an equivalent electrical signal for further processing or transmission.

True or false

37.In a basic communication system block diagram, the destination is the point where the original information is finally used or understood by the receiver of the message.

Answer: True

The destination represents the end-user or device that receives and makes use of the reconstructed information signal after it passes through the receiver.

Multiple choice

38.Bandwidth, in the context of communication systems, refers to

  • Athe physical thickness of a transmission cable
  • Bthe range of frequencies that a channel or signal occupies or can carry
  • Cthe total distance a signal can travel
  • Dthe number of receivers connected to a channel

Answer: B

Bandwidth is the width of the frequency range that a signal occupies or that a communication channel is able to carry.

Multiple choice

39.Compared to AM radio, FM radio generally requires

  • Aa wider bandwidth, but can provide higher quality (less noisy) audio
  • Bno bandwidth at all
  • Can identical bandwidth in all cases
  • Da narrower bandwidth and lower audio quality

Answer: A

FM signals typically occupy a wider bandwidth than AM signals, but this trade-off provides greater resistance to noise and higher fidelity audio reproduction.

Multiple choice

40.Satellite communication systems are a modern type of communication system that primarily rely on

  • Ahand-delivered written letters
  • Bsound waves travelling through the atmosphere
  • Cunderground fibre-optic cables exclusively
  • Drelaying signals via satellites orbiting the Earth to cover very long distances, including across oceans and remote areas

Answer: D

Communication satellites receive signals from a ground station, amplify them, and retransmit them to another location, enabling long-distance and remote-area communication that ground-based systems could not easily provide.

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Unit 9: Magnetic Field and Magnetic Forces

Multiple choice

1.What is a magnetic field?

  • AA region of space where an electric charge experiences a force due to its charge alone
  • BA region of space around a magnet or current-carrying conductor where a magnetic force can be detected on another magnet or moving charge
  • CThe space occupied by a stationary magnet only
  • DA field that exists only inside conducting wires

Answer: B

A magnetic field is the region around a magnet or current-carrying conductor in which a force is exerted on other magnets, magnetic materials, or moving charges.

Multiple choice

2.Which of the following is NOT a property of magnetic field lines?

  • AThey emerge from the north pole and enter the south pole outside the magnet
  • BThey form closed loops
  • CThey never intersect each other
  • DThey can cross each other at points of zero field strength

Answer: D

Magnetic field lines never intersect anywhere, since a crossing point would imply two directions of the field at the same point, which is impossible.

Multiple choice

3.Outside a bar magnet, magnetic field lines point:

  • AFrom south pole to north pole
  • BFrom north pole to south pole
  • CPerpendicular to the magnet's axis only
  • DRandomly in all directions

Answer: B

By convention, magnetic field lines emerge from the north pole and travel through the external space to the south pole, then continue inside the magnet from south to north.

Multiple choice

4.According to the right-hand grip rule, if a straight wire carries current upward, the magnetic field lines around it form:

  • AStraight lines parallel to the wire
  • BRadial lines pointing away from the wire
  • CConcentric circles in a plane perpendicular to the wire, counter-clockwise when viewed from above
  • DConcentric circles, clockwise when viewed from above

Answer: C

Gripping the wire with the right thumb pointing in the direction of current flow, the curled fingers give the direction of the circular field lines; viewed from above with current going up, they appear counter-clockwise.

Multiple choice

5.The magnetic field at a perpendicular distance r from a long straight current-carrying wire carrying current I is given by:

  • AB = μ₀Ir/(2π)
  • BB = μ₀nI
  • CB = μ₀I/(2r)
  • DB = μ₀I/(2πr)

Answer: D

The magnetic field around an infinite straight conductor is B = μ₀I/(2πr), decreasing inversely with distance from the wire.

Multiple choice

6.A long straight wire carries a current of 10 A. What is the magnetic field at a perpendicular distance of 5 cm from the wire? (μ₀ = 4π×10⁻⁷ T·m/A)

  • A4 × 10⁻⁴ T
  • B8 × 10⁻⁵ T
  • C4 × 10⁻⁵ T
  • D4 × 10⁻⁶ T

Answer: C

B = μ₀I/(2πr) = (4π×10⁻⁷ × 10)/(2π × 0.05) = (2×10⁻⁶)/(0.05) = 4 × 10⁻⁵ T.

Multiple choice

7.The magnetic field inside a long, tightly-wound solenoid carrying current I with n turns per unit length is given by:

  • AB = μ₀n/I
  • BB = μ₀nI
  • CB = μ₀I²n
  • DB = μ₀I/(2πr)

Answer: B

For an ideal long solenoid, the field inside is uniform and given by B = μ₀nI, where n is the number of turns per unit length.

Multiple choice

8.A solenoid of length 0.5 m has 500 turns and carries a current of 2 A. Find the magnetic field inside it. (μ₀ = 4π×10⁻⁷ T·m/A)

  • A1.0 × 10⁻³ T
  • B5.0 × 10⁻³ T
  • C2.5 × 10⁻³ T
  • D2.5 × 10⁻⁴ T

Answer: C

n = N/l = 500/0.5 = 1000 turns/m. B = μ₀nI = 4π×10⁻⁷ × 1000 × 2 = 2.51 × 10⁻³ T.

Multiple choice

9.Doubling the number of turns per unit length of a solenoid (keeping current constant) causes the magnetic field inside it to:

  • AQuadruple
  • BRemain unchanged
  • CHalve
  • DDouble

Answer: D

Since B = μ₀nI, the field is directly proportional to n, so doubling n doubles B.

Multiple choice

10.The magnetic field pattern inside a current-carrying solenoid closely resembles the field of:

  • AA point charge
  • BTwo like poles facing each other
  • CA straight current-carrying wire
  • DA bar magnet

Answer: D

A solenoid produces a fairly uniform field inside, similar in shape to the field of a bar magnet, with one end acting as a north pole and the other as a south pole.

Multiple choice

11.Magnetic flux through a surface of area A in a uniform field B, where θ is the angle between B and the normal to the surface, is given by:

  • AΦ = BA tanθ
  • BΦ = BA cosθ
  • CΦ = BA/θ
  • DΦ = BA sinθ

Answer: B

Magnetic flux is Φ = BA cosθ, where θ is measured between the field direction and the normal (perpendicular) to the surface.

Multiple choice

12.Magnetic flux through a loop is maximum when:

  • AThe field is parallel to the plane of the loop
  • BThe field is at 45° to the normal
  • CThe loop area is zero
  • DThe field is perpendicular to the plane of the loop (parallel to the normal)

Answer: D

Flux Φ = BA cosθ is maximum (Φ = BA) when θ = 0°, i.e. when B is along the normal to the loop, meaning B is perpendicular to the plane of the loop.

Multiple choice

13.The SI unit of magnetic flux is the:

  • AHenry
  • BWeber
  • CAmpere-turn
  • DTesla

Answer: B

Magnetic flux is measured in Weber (Wb), where 1 Wb = 1 T·m².

Multiple choice

14.The force on a straight current-carrying conductor of length L carrying current I in a uniform magnetic field B, making angle θ with the field, is:

  • AF = BIL
  • BF = BI/L sinθ
  • CF = BIL sinθ
  • DF = BIL cosθ

Answer: C

The force on a current-carrying conductor in a magnetic field is F = BIL sinθ, where θ is the angle between the current direction and the field.

Multiple choice

15.A wire of length 0.3 m carrying a current of 5 A is placed perpendicular to a magnetic field of 0.2 T. Calculate the force on the wire.

  • A0.3 N
  • B0.4 N
  • C0.2 N
  • D0.1 N

Answer: A

Since the wire is perpendicular to B, θ = 90°, so F = BIL sinθ = 0.2 × 5 × 0.3 × 1 = 0.3 N.

Multiple choice

16.The force on a current-carrying conductor placed in a magnetic field is maximum when the angle between the current and the field is:

  • A0°
  • B180°
  • C90°
  • D45°

Answer: C

Since F = BIL sinθ, the force is maximum when sinθ = 1, i.e. θ = 90°, meaning the conductor is perpendicular to the field.

Multiple choice

17.The direction of the force on a current-carrying conductor in a magnetic field is best determined using:

  • AFleming's left-hand rule
  • BKirchhoff's law
  • CFleming's right-hand rule
  • DLenz's law

Answer: A

Fleming's left-hand rule gives the direction of the force: with the thumb, first finger, and second finger mutually at right angles, the First finger points along the magnetic Field, the seCond finger along the Current, and the thuMb gives the direction of the resulting Motion (force).

Multiple choice

18.The magnetic force on a charge q moving with velocity v at angle θ to a magnetic field B is given by:

  • AF = qv/B sinθ
  • BF = qvB cosθ
  • CF = qvB sinθ
  • DF = qvB

Answer: C

The magnetic force on a moving charge is F = qvB sinθ, where θ is the angle between the velocity vector and the magnetic field.

Multiple choice

19.An electron (q = 1.6×10⁻¹⁹ C) moves at 2×10⁶ m/s perpendicular to a magnetic field of 0.5 T. What is the magnitude of the magnetic force on it?

  • A1.6 × 10⁻¹³ N
  • B8.0 × 10⁻¹⁴ N
  • C1.6 × 10⁻¹⁴ N
  • D3.2 × 10⁻¹³ N

Answer: A

F = qvB sinθ = (1.6×10⁻¹⁹)(2×10⁶)(0.5)(sin90°) = 1.6 × 10⁻¹³ N.

Multiple choice

20.A charged particle moving parallel to a magnetic field experiences:

  • AZero force
  • BForce perpendicular to both v and B always
  • CA force equal to qvB
  • DMaximum force

Answer: A

Since F = qvB sinθ, when the velocity is parallel to B (θ = 0°), sinθ = 0, so the force is zero.

Multiple choice

21.A charged particle moving in a uniform magnetic field, with velocity always perpendicular to B, moves in a:

  • AStraight line
  • BParabolic path
  • CElliptical path
  • DCircular path

Answer: D

When the magnetic force is always perpendicular to velocity, it acts as a centripetal force, causing the charge to move in a circle of radius r = mv/(qB).

Multiple choice

22.An electron (m = 9.11×10⁻³¹ kg, q = 1.6×10⁻¹⁹ C) moves at 1×10⁶ m/s perpendicular to a 0.2 T field. Find the radius of its circular path.

  • A5.7 × 10⁻⁶ m
  • B2.85 × 10⁻⁵ m
  • C1.14 × 10⁻⁴ m
  • D9.11 × 10⁻⁵ m

Answer: B

r = mv/(qB) = (9.11×10⁻³¹ × 1×10⁶)/(1.6×10⁻¹⁹ × 0.2) = (9.11×10⁻²⁵)/(3.2×10⁻²⁰) ≈ 2.85 × 10⁻⁵ m.

Multiple choice

23.In a simple DC motor, the split-ring commutator serves to:

  • AReduce friction between the coil and brushes
  • BIncrease the strength of the magnetic field
  • CStore electrical energy
  • DReverse the direction of current in the coil every half rotation, keeping the torque in the same rotational sense

Answer: D

The split-ring commutator reverses the current direction in the coil every half turn so that the torque produced always acts in the same rotational direction, allowing continuous rotation.

Multiple choice

24.In a DC motor, the carbon brushes function to:

  • AMaintain electrical contact between the external circuit and the rotating commutator
  • BConvert AC to DC before it enters the motor
  • CGenerate the magnetic field
  • DProvide mechanical support for the axle only

Answer: A

Brushes are stationary conductors (often carbon) that press against the rotating commutator to maintain continuous electrical contact between the external circuit and the armature coil.

Multiple choice

25.The basic structure of a simple DC motor includes all of the following EXCEPT:

  • AA capacitor connected in series with the coil
  • BA split-ring commutator with brushes
  • CA coil (armature) of wire
  • DPermanent magnets or field magnets

Answer: A

A simple DC motor consists of a rotating coil, a magnetic field (from permanent or field magnets), and a split-ring commutator with brushes; a series capacitor is not part of its basic structure.

Multiple choice

26.The torque on a current-carrying rectangular coil of N turns, area A, carrying current I in a field B, when the plane of the coil is parallel to B, is given by:

  • Aτ = NBIA/2
  • Bτ = 0
  • Cτ = NBIA
  • Dτ = NBI/A

Answer: C

Torque is τ = NBIA sinφ where φ is the angle between the plane of the coil and B; when the coil plane is parallel to B, φ = 90°, so τ = NBIA (maximum torque).

Multiple choice

27.A rectangular coil with N = 100 turns, area 0.02 m², carries a current of 2 A in a field of 0.1 T. Find the maximum torque on the coil.

  • A0.2 N·m
  • B0.4 N·m
  • C0.04 N·m
  • D4.0 N·m

Answer: B

Maximum torque: τ = NBIA = 100 × 0.1 × 2 × 0.02 = 0.4 N·m.

Multiple choice

28.Increasing the number of turns in the coil of a DC motor (all else constant) will:

  • AIncrease the torque produced
  • BReverse the direction of rotation
  • CDecrease the torque produced
  • DHave no effect on torque

Answer: A

Since torque τ = NBIA sinφ, torque is directly proportional to the number of turns N, so increasing N increases the torque.

Multiple choice

29.In a DC motor, the permanent (field) magnets are primarily responsible for:

  • AProducing the external uniform magnetic field in which the coil rotates
  • BReducing electrical resistance in the circuit
  • CConverting mechanical energy into electrical energy
  • DReversing the current every half cycle

Answer: A

The field magnets (permanent magnets or electromagnets) provide the magnetic field that interacts with the current in the coil to produce the force and hence the torque that rotates the motor.

Multiple choice

30.A DC motor converts:

  • AMagnetic energy into chemical energy
  • BElectrical energy into mechanical energy
  • CMechanical energy into electrical energy
  • DChemical energy into thermal energy

Answer: B

A DC motor operates on the principle that a current-carrying coil in a magnetic field experiences a torque, converting electrical energy into mechanical (rotational) energy.

True or false

31.Magnetic field lines can intersect at points where the field strength is zero.

Answer: False

Magnetic field lines never intersect anywhere; a crossing point would imply two different field directions at the same location, which is physically impossible.

True or false

32.A charged particle moving parallel to a magnetic field experiences zero magnetic force.

Answer: True

Since F = qvB sinθ, when θ = 0° (velocity parallel to B), sinθ = 0 and the force is zero.

True or false

33.The magnetic field around a long straight wire decreases as the distance from the wire increases.

Answer: True

B = μ₀I/(2πr) shows that the field strength is inversely proportional to the perpendicular distance r from the wire.

True or false

34.In a DC motor, the split-ring commutator reverses the direction of current in the coil every half rotation.

Answer: True

This reversal keeps the torque acting in the same rotational sense each half-turn, allowing the motor to continue rotating in one direction.

True or false

35.Magnetic flux through a surface does not depend on the angle between the magnetic field and the normal to the surface.

Answer: False

Magnetic flux is Φ = BA cosθ, which clearly depends on the angle θ between the field and the normal to the surface.

Fill in the blank

36.The device in a DC motor that reverses the direction of current in the coil every half rotation is called the ______.

Answer: split-ring commutator

The split-ring commutator reverses the current direction each half turn so the torque continues to act in the same rotational sense.

Fill in the blank

37.The SI unit of magnetic flux is the ______.

Answer: weber (Wb)

Magnetic flux Φ = BA cosθ is measured in webers, where 1 Wb = 1 T·m².

Fill in the blank

38.The magnetic field inside a long, ideal solenoid is ______ and directed along its axis.

Answer: uniform

Inside a long solenoid, the field is nearly uniform in magnitude and direction, unlike the field outside which is weak and non-uniform.

Fill in the blank

39.The SI unit of magnetic field strength (magnetic flux density) is the ______.

Answer: tesla (T)

Magnetic field strength B is measured in tesla, where 1 T = 1 Wb/m² = 1 N/(A·m).

Fill in the blank

40.The magnetic force on a moving charge is given by the equation F = ______.

Answer: qvB sinθ

The magnitude of the force on a charge q moving with speed v at angle θ to a field B is F = qvB sinθ.

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Unit 10: Introduction to the Special Theory of Relativity

Multiple choice

1.The theory of relativity is primarily concerned with:

  • AHow measurements of space, time, and motion depend on the relative motion of observers
  • BHow chemical reactions proceed at high temperatures
  • CHow electric charges interact at rest
  • DHow sound waves travel through different media

Answer: A

Relativity studies how quantities such as time, length, mass, and simultaneity are measured differently by observers in relative motion to one another.

Multiple choice

2.An inertial reference frame is one that:

  • AIs always attached to the Earth's surface
  • BRotates at constant angular speed
  • CIs at rest or moving with constant velocity (zero net acceleration)
  • DIs accelerating uniformly

Answer: C

An inertial frame is a non-accelerating frame — one that is either at rest or moving with constant velocity — in which Newton's first law holds.

Multiple choice

3.According to the Galilean transformation, if frame S' moves with velocity v along the x-axis relative to frame S, the position x' in S' is given by:

  • Ax' = x − vt
  • Bx' = vt − x
  • Cx' = x + vt
  • Dx' = x/vt

Answer: A

The Galilean transformation gives x' = x − vt (and y' = y, z' = z, t' = t), relating coordinates in the moving frame to those in the stationary frame.

Multiple choice

4.In the Galilean transformation, time is assumed to be:

  • ADependent on the observer's velocity
  • BUndefined for moving frames
  • CDifferent in every reference frame
  • DAbsolute and the same in all reference frames (t' = t)

Answer: D

Classical (Galilean) relativity assumes time is absolute — it flows the same way for all observers regardless of their relative motion, so t' = t.

Multiple choice

5.According to the Galilean velocity addition rule, if a ball is thrown forward at speed u inside a train moving at speed v (relative to the ground), its speed relative to the ground is:

  • Au/v
  • Bu + v
  • Cv − u
  • Du − v

Answer: B

Galilean relativity simply adds velocities: the ground observer sees the ball moving at u + v, since velocities are assumed to combine additively.

Multiple choice

6.The first postulate of Einstein's special theory of relativity states that:

  • AThe laws of physics are the same in all inertial reference frames
  • BMass increases without limit at low speeds
  • CTime is absolute for all observers
  • DThe speed of light depends on the observer's motion

Answer: A

Einstein's first postulate (principle of relativity) states that the laws of physics take the same form in every inertial reference frame.

Multiple choice

7.The second postulate of Einstein's special theory of relativity states that:

  • AThe speed of light varies depending on the observer's velocity
  • BThe speed of light in vacuum is the same for all observers, regardless of the motion of the source or observer
  • CLight travels faster in a moving frame
  • DLight needs a medium (ether) to propagate

Answer: B

Einstein proposed that the speed of light in vacuum (c ≈ 3×10⁸ m/s) is constant and the same for every inertial observer, independent of the relative motion of the source or observer.

Multiple choice

8.Which experimental result motivated Einstein's postulate about the speed of light?

  • AThe photoelectric effect
  • BThe Michelson–Morley experiment, which found no evidence of a luminiferous ether or variation in the speed of light
  • CRutherford's gold foil experiment
  • DYoung's double-slit experiment

Answer: B

The Michelson–Morley experiment failed to detect any variation in the speed of light due to Earth's motion through a hypothesized ether, supporting the idea that c is constant for all observers.

Multiple choice

9.One major implication of Einstein's postulates is that:

  • ASimultaneity of events is relative — two events simultaneous in one frame may not be simultaneous in another
  • BSimultaneity of events is absolute for all observers
  • CMass and energy are unrelated
  • DTime and space are completely independent of motion

Answer: A

Because the speed of light is constant for all observers, events that appear simultaneous in one inertial frame may not appear simultaneous to an observer in a different inertial frame moving relative to the first.

Multiple choice

10.The Lorentz factor γ is defined as:

  • Aγ = v²/c²
  • Bγ = 1 − v²/c²
  • Cγ = 1/√(1 − v²/c²)
  • Dγ = √(1 − v²/c²)

Answer: C

The Lorentz factor is γ = 1/√(1 − v²/c²), which appears in the equations for time dilation, length contraction, and relativistic mass/energy.

Multiple choice

11.Calculate the Lorentz factor γ for an object moving at v = 0.6c.

  • A1.00
  • B2.00
  • C1.67
  • D1.25

Answer: D

γ = 1/√(1 − v²/c²) = 1/√(1 − 0.36) = 1/√0.64 = 1/0.8 = 1.25.

Multiple choice

12.Time dilation is described by the equation:

  • AΔt = Δt₀ √(1 − v²/c²)
  • BΔt = Δt₀ v/c
  • CΔt = Δt₀/√(1 − v²/c²)
  • DΔt = Δt₀(1 − v²/c²)

Answer: C

Time dilation states that the time interval Δt measured by an observer for whom the clock is moving is Δt = γΔt₀ = Δt₀/√(1 − v²/c²), where Δt₀ is the proper time.

Multiple choice

13.A clock on a spaceship measures a proper time interval of 2 s between two events. If the spaceship moves at v = 0.6c relative to Earth, what time interval does an Earth observer measure?

  • A3.2 s
  • B2.5 s
  • C2.0 s
  • D1.6 s

Answer: B

γ = 1.25 for v = 0.6c, so Δt = γΔt₀ = 1.25 × 2 s = 2.5 s.

Multiple choice

14.As observed from a stationary (Earth) frame, a clock moving at high speed relative to that frame appears to:

  • ARun slower than an identical stationary clock
  • BStop completely at any nonzero speed
  • CRun at exactly the same rate
  • DRun faster than an identical stationary clock

Answer: A

Time dilation implies that a moving clock, as observed from a stationary frame, ticks more slowly (runs slower) than an identical stationary clock, since Δt = γΔt₀ > Δt₀.

Multiple choice

15.Proper time (Δt₀) is defined as the time interval between two events:

  • AMeasured by an observer for whom the two events occur at the same location (at rest relative to the events)
  • BThat is always longer than the time measured in any other frame
  • CMeasured by any observer, regardless of motion
  • DMeasured only on Earth

Answer: A

Proper time is the time interval measured by a clock that is present at both events, i.e. at rest relative to the events, and it is always the shortest time interval measured between two events.

Multiple choice

16.Length contraction is described by the equation:

  • AL = L₀ γ
  • BL = L₀(1 + v²/c²)
  • CL = L₀/√(1 − v²/c²)
  • DL = L₀ √(1 − v²/c²)

Answer: D

The length of a moving object, as measured by an observer relative to whom it is moving, is contracted: L = L₀√(1 − v²/c²) = L₀/γ, where L₀ is the proper length.

Multiple choice

17.A spaceship has a proper length of 100 m. What length would an observer on Earth measure if the ship travels at v = 0.8c?

  • A60 m
  • B80 m
  • C40 m
  • D100 m

Answer: A

γ = 1/√(1 − 0.64) = 1/√0.36 = 1/0.6 ≈ 1.667. L = L₀/γ = 100/1.667 = 60 m.

Multiple choice

18.Length contraction occurs:

  • AOnly perpendicular to the direction of motion
  • BOnly along the direction of relative motion
  • COnly when the object is accelerating
  • DIn all three spatial dimensions equally

Answer: B

Length contraction affects only the dimension of an object that lies along the direction of relative motion; dimensions perpendicular to the motion are unaffected.

Multiple choice

19.The proper length of an object is:

  • AThe length measured in the reference frame in which the object is at rest
  • BThe length measured by an observer moving relative to the object
  • CAlways shorter than the length measured by a moving observer
  • DUndefined in special relativity

Answer: A

Proper length L₀ is the length of an object as measured in its own rest frame; any observer moving relative to the object measures a shorter (contracted) length.

Multiple choice

20.Einstein's mass-energy equivalence relation is expressed as:

  • AE = m²c
  • BE = mc
  • CE = mc²
  • DE = m/c²

Answer: C

Einstein showed that mass and energy are equivalent and related by E = mc², where c is the speed of light in vacuum.

Multiple choice

21.Calculate the energy equivalent of a mass of 1 gram (1 × 10⁻³ kg) using E = mc² (c = 3 × 10⁸ m/s).

  • A3 × 10⁸ J
  • B9 × 10¹⁶ J
  • C9 × 10¹³ J
  • D9 × 10¹⁰ J

Answer: C

E = mc² = (1×10⁻³)(3×10⁸)² = (1×10⁻³)(9×10¹⁶) = 9 × 10¹³ J.

Multiple choice

22.A nuclear reaction releases 1.8 × 10⁻¹⁰ J of energy due to a mass defect. What is the mass defect (c = 3 × 10⁸ m/s)?

  • A1.8 × 10⁻²⁶ kg
  • B6 × 10⁻¹⁹ kg
  • C5.4 × 10⁻³ kg
  • D2 × 10⁻²⁷ kg

Answer: D

From E = mc², m = E/c² = (1.8×10⁻¹⁰)/(9×10¹⁶) = 2 × 10⁻²⁷ kg.

Multiple choice

23.One implication of E = mc² is that:

  • AOnly chemical reactions can release the energy equivalent of mass
  • BMass can be converted into energy and energy into mass
  • CMass and energy are completely unrelated quantities
  • DEnergy can never be released from matter

Answer: B

Mass-energy equivalence means mass and energy are interchangeable forms of the same physical quantity, as seen in nuclear fission, fusion, and particle-antiparticle annihilation.

Multiple choice

24.According to special relativity, as the speed of an object with nonzero rest mass approaches the speed of light, the energy required to accelerate it further:

  • AApproaches zero
  • BApproaches a finite constant value
  • CDecreases steadily
  • DApproaches infinity

Answer: D

As v → c, the Lorentz factor γ → ∞, so the relativistic energy (and the energy needed to further accelerate the object) also approaches infinity, which is why massive objects cannot reach the speed of light.

Multiple choice

25.The relativity of simultaneity means that:

  • ASimultaneity has no meaning in physics
  • BTwo events that are simultaneous for one inertial observer may not be simultaneous for another observer in relative motion
  • COnly events at the same location can be simultaneous
  • DAll observers always agree on which events are simultaneous

Answer: B

Because of the finite, constant speed of light, whether two spatially separated events are simultaneous depends on the observer's frame of reference — this is the relativity of simultaneity.

Multiple choice

26.In the twin paradox, a twin who travels on a high-speed round trip and returns to Earth, compared to the twin who stayed on Earth, will be:

  • AOlder than the twin who stayed on Earth
  • BExactly the same age
  • CUnable to be compared due to relativity
  • DYounger than the twin who stayed on Earth

Answer: D

Due to time dilation, the traveling twin's clock (proper time along their path) accumulates less elapsed time, so upon return they are younger than the twin who remained on Earth.

Multiple choice

27.GPS satellite clocks must be corrected for relativistic effects mainly because:

  • ARadio waves travel faster in space than on Earth
  • BSatellites do not use electromagnetic signals
  • CSatellites move at high speed and are in a different gravitational potential, both of which affect their clock rates relative to clocks on Earth
  • DGPS relies only on Newtonian mechanics

Answer: C

GPS satellites move at high orbital speeds (special relativistic time dilation) and experience weaker gravity (general relativistic effect), both of which cause their onboard clocks to run at a different rate than clocks on Earth, requiring correction.

Multiple choice

28.As v increases from 0 toward c, the Lorentz factor γ:

  • ARemains constant at 1
  • BDecreases from 1 toward 0
  • CIncreases from 1 toward infinity
  • DOscillates periodically

Answer: C

Since γ = 1/√(1 − v²/c²), as v increases toward c, the denominator approaches zero, so γ increases without bound toward infinity.

Multiple choice

29.A rod has a rest length of 50 m. Measured by an observer relative to whom it moves at v = 0.6c, its length is:

  • A30 m
  • B50 m
  • C62.5 m
  • D40 m

Answer: D

γ = 1.25 for v = 0.6c. L = L₀/γ = 50/1.25 = 40 m.

Multiple choice

30.Which statement correctly compares Galilean and Einsteinian relativity?

  • ABoth assume time is absolute
  • BGalilean relativity assumes absolute time and unlimited relative speeds; Einsteinian relativity treats time as relative and limits speeds to at most c
  • CGalilean relativity accounts for the constancy of the speed of light
  • DEinsteinian relativity applies only to slow-moving objects

Answer: B

Galilean relativity assumes time is universal and speeds simply add without limit, while Einstein's relativity shows time and length are relative to the observer and no material object can reach or exceed the speed of light.

True or false

31.According to the Galilean transformation, time is assumed to be the same for all observers, regardless of their relative motion.

Answer: True

Classical (Galilean) relativity treats time as absolute, so t' = t in all inertial frames — an assumption later shown to be incorrect by special relativity.

True or false

32.According to Einstein's postulates, the speed of light in vacuum depends on the velocity of the source emitting it.

Answer: False

Einstein's second postulate states that the speed of light in vacuum is constant for all inertial observers, independent of the motion of the source or the observer.

True or false

33.As observed from a stationary frame, a moving clock runs faster than an identical stationary clock.

Answer: False

Time dilation predicts the opposite: a moving clock, as seen from a stationary frame, runs slower (Δt = γΔt₀ > Δt₀ for the stationary observer's measurement of the moving clock's ticks).

True or false

34.Length contraction occurs only in the direction perpendicular to the relative motion between observer and object.

Answer: False

Length contraction occurs only along the direction of relative motion; dimensions perpendicular to the motion remain unchanged.

True or false

35.According to Einstein's mass-energy equivalence, mass and energy are interchangeable forms of the same physical quantity.

Answer: True

E = mc² shows that mass can be converted into energy and vice versa, as observed in nuclear reactions and particle physics.

Fill in the blank

36.The equation E = ______ expresses the equivalence of mass and energy.

Answer: mc²

Einstein's mass-energy equivalence relation is E = mc², where c is the speed of light in vacuum.

Fill in the blank

37.A reference frame that is at rest or moving at constant velocity is called an ______ frame.

Answer: inertial

An inertial frame is a non-accelerating frame of reference in which Newton's first law (and the postulates of special relativity) holds.

Fill in the blank

38.The fact that two events simultaneous in one reference frame may not be simultaneous in another moving frame is called the relativity of ______.

Answer: simultaneity

This effect, called the relativity of simultaneity, arises because the speed of light is constant and signals take time to travel between observers in relative motion.

Fill in the blank

39.The factor γ = 1/√(1 − v²/c²) used in time dilation and length contraction equations is called the ______ factor.

Answer: Lorentz

This quantity, the Lorentz factor, increases from 1 toward infinity as an object's speed approaches the speed of light.

Fill in the blank

40.According to length contraction, an object's length is greatest (equal to its proper length) when measured in its own ______ frame.

Answer: rest

The proper length L₀ is measured in the object's rest frame; any observer moving relative to the object measures a shorter, contracted length.

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Unit 11: Interference and Diffraction of Light

Multiple choice

1.An electromagnetic wave is best described as:

  • AA transverse wave consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation
  • BA mechanical wave that transports matter
  • CA longitudinal wave requiring a material medium to travel
  • DA wave that only exists inside conductors

Answer: A

Electromagnetic waves are transverse waves made up of oscillating electric and magnetic fields that are perpendicular to each other and to the direction the wave travels, and they can propagate through vacuum.

Multiple choice

2.Electromagnetic waves can travel through:

  • AOnly solids
  • BVacuum, as well as through various media
  • COnly gases
  • DOnly liquids

Answer: B

Unlike mechanical waves, electromagnetic waves do not need a medium; they can propagate through vacuum as well as through transparent media such as air, water, and glass.

Multiple choice

3.The speed of electromagnetic waves in a vacuum is approximately:

  • A3 × 10¹⁰ m/s
  • B3 × 10⁸ m/s
  • C3 × 10⁶ m/s
  • D3 × 10⁵ m/s

Answer: B

All electromagnetic waves travel at the speed of light in vacuum, c ≈ 3 × 10⁸ m/s, regardless of their frequency or wavelength.

Multiple choice

4.Arranged in order of increasing frequency, the electromagnetic spectrum is:

  • ARadio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays
  • BVisible, infrared, radio waves, microwaves, ultraviolet, X-rays, gamma rays
  • CGamma rays, X-rays, ultraviolet, visible, infrared, microwave, radio waves
  • DRadio waves, gamma rays, X-rays, visible, infrared, microwaves, ultraviolet

Answer: A

In order of increasing frequency (decreasing wavelength), the spectrum runs radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, then gamma rays.

Multiple choice

5.Which region of the electromagnetic spectrum is commonly used for medical imaging of bones due to its high penetrating power?

  • AMicrowaves
  • BX-rays
  • CRadio waves
  • DInfrared

Answer: B

X-rays have high energy and penetrating power, allowing them to pass through soft tissue but be absorbed by denser material like bone, making them useful for medical imaging.

Multiple choice

6.Microwaves are commonly applied in:

  • AProducing visible light in incandescent bulbs
  • BSterilizing surgical instruments using ionizing radiation
  • CRadiotherapy for cancer treatment only
  • DSatellite and mobile communication, and microwave cooking

Answer: D

Microwaves are widely used in communication systems (mobile phones, satellites, radar) and in microwave ovens, where they cause water molecules in food to vibrate and generate heat.

Multiple choice

7.For two light sources to produce a sustained (observable) interference pattern, they must be:

  • APlaced very far apart
  • BCoherent — having a constant phase difference and the same frequency
  • CExtremely bright
  • DOf different frequencies

Answer: B

Interference patterns remain stable only if the two sources are coherent, meaning they emit waves of the same frequency with a constant (unchanging) phase difference.

Multiple choice

8.Constructive interference occurs at points where the path difference between two coherent waves is:

  • AExactly a quarter wavelength
  • BAn integral multiple of the wavelength (nλ)
  • CAn odd multiple of half the wavelength
  • DAny random value

Answer: B

Constructive interference (bright fringes) occurs when the path difference equals a whole number of wavelengths: Δ = nλ, where n = 0, ±1, ±2, ...

Multiple choice

9.Destructive interference occurs at points where the path difference between two coherent waves is:

  • AAn odd multiple of half the wavelength, i.e. (n + 1/2)λ
  • BZero
  • CAn integral multiple of the wavelength
  • DEqual to the slit separation

Answer: A

Destructive interference (dark fringes) occurs when the path difference is an odd multiple of half a wavelength: Δ = (n + 1/2)λ, causing the waves to arrive out of phase and cancel.

Multiple choice

10.Why can't two independent light bulbs produce a stable interference pattern?

  • AThe distance between bulbs is always too large
  • BTheir light waves have random, rapidly changing phase differences (they are incoherent)
  • CLight bulbs emit no electromagnetic waves
  • DThey emit light of exactly the same wavelength

Answer: B

Independent sources emit light with randomly and rapidly varying phase relationships (incoherent light), so any interference pattern shifts too fast to be observed, averaging out to uniform illumination.

Multiple choice

11.In Young's double-slit experiment, the two coherent sources are typically obtained by:

  • AIlluminating two narrow, closely spaced slits with light from a single source
  • BUsing a prism to split white light into colors
  • CUsing two separate, unrelated lamps
  • DReflecting light off a mirror twice

Answer: A

Young's experiment achieves coherence by passing light from a single source through two narrow slits, so that the light emerging from both slits maintains a constant phase relationship.

Multiple choice

12.In Young's double-slit experiment, the fringe spacing (fringe width) β is given by:

  • Aβ = λD/d
  • Bβ = dD/λ
  • Cβ = λd/D
  • Dβ = D/(λd)

Answer: A

The fringe spacing in Young's double-slit experiment is β = λD/d, where λ is the wavelength, D is the distance from slits to screen, and d is the slit separation.

Multiple choice

13.In a Young's double-slit setup, λ = 600 nm, D = 1 m, and d = 1 mm. Calculate the fringe width.

  • A6 mm
  • B60 mm
  • C0.6 mm
  • D0.06 mm

Answer: C

β = λD/d = (600×10⁻⁹ × 1)/(1×10⁻³) = 6 × 10⁻⁴ m = 0.6 mm.

Multiple choice

14.If the slit separation d in Young's double-slit experiment is increased while λ and D stay constant, the fringe width:

  • ABecomes infinite
  • BRemains the same
  • CIncreases
  • DDecreases

Answer: D

Since β = λD/d, fringe width is inversely proportional to slit separation d, so increasing d decreases the fringe width.

Multiple choice

15.If the wavelength of light used in Young's double-slit experiment is increased (D and d fixed), the fringe width will:

  • ADecrease
  • BBecome zero
  • CIncrease
  • DStay the same

Answer: C

Since β = λD/d, fringe width is directly proportional to wavelength, so a longer wavelength produces wider fringes.

Multiple choice

16.Increasing the distance D between the double slit and the screen, with λ and d constant, causes the fringe width to:

  • ABecome negative
  • BRemain unchanged
  • CDecrease
  • DIncrease

Answer: D

Since β = λD/d, fringe width increases directly with the slit-to-screen distance D.

Multiple choice

17.In Young's double-slit pattern, the central bright fringe occurs where:

  • AThere is no light from either slit
  • BThe path difference equals one wavelength
  • CThe path difference is zero
  • DThe path difference equals half a wavelength

Answer: C

The central fringe is bright because the path difference from both slits to that point on the screen is zero, giving perfect constructive interference (n = 0).

Multiple choice

18.The condition for bright fringes in a double-slit experiment, in terms of slit separation d and angle θ from the central axis, is:

  • Ad cosθ = nλ
  • Bd sinθ = (n + 1/2)λ
  • Cd sinθ = nλ
  • Dd tanθ = nλ/2

Answer: C

Bright fringes occur where the path difference d sinθ equals a whole number of wavelengths: d sinθ = nλ, for n = 0, ±1, ±2, ...

Multiple choice

19.In the intensity distribution formula for double-slit interference, I = 4I₀cos²(φ/2), where I₀ is the intensity from a single slit, the maximum resultant intensity is:

  • A2I₀
  • BI₀
  • C8I₀
  • D4I₀

Answer: D

The maximum intensity occurs when cos²(φ/2) = 1 (at φ = 0, 2π, ...), giving I_max = 4I₀, four times the intensity of a single slit alone.

Multiple choice

20.According to the intensity distribution of the double-slit fringe pattern, the intensity is zero (dark fringe) when the phase difference φ equals:

  • A2π
  • B0
  • Cπ (and odd multiples of π)
  • D4π

Answer: C

I = 4I₀cos²(φ/2) is zero when cos(φ/2) = 0, which occurs at φ/2 = π/2, 3π/2, ..., i.e. φ = π, 3π, 5π, ... (odd multiples of π).

Multiple choice

21.The relationship between phase difference φ and path difference Δ for two interfering waves of wavelength λ is:

  • Aφ = (λ/2π)Δ
  • Bφ = (2π/λ)Δ
  • Cφ = λΔ
  • Dφ = Δ/λ

Answer: B

Phase difference and path difference are related by φ = (2π/λ) × Δ, since a path difference of one full wavelength corresponds to a phase difference of 2π.

Multiple choice

22.Two coherent waves have a path difference of λ/2. What is their phase difference?

  • A0 rad
  • Bπ rad
  • C2π rad
  • Dπ/2 rad

Answer: B

φ = (2π/λ)Δ = (2π/λ)(λ/2) = π rad, which corresponds to destructive interference.

Multiple choice

23.Diffraction of light refers to:

  • AThe bending or spreading of light waves around obstacles or through small apertures
  • BThe absorption of light by a black surface
  • CThe reflection of light from a mirror
  • DThe splitting of white light into its component colors by a prism

Answer: A

Diffraction is the bending and spreading of waves as they pass around an obstacle or through a narrow aperture (slit), most noticeable when the obstacle/aperture size is comparable to the wavelength.

Multiple choice

24.Diffraction effects become most noticeable when the size of the slit or obstacle is:

  • AComparable to (of the same order as) the wavelength of light
  • BMuch smaller than the wavelength of light
  • CExactly equal to zero
  • DMuch larger than the wavelength of light

Answer: A

Diffraction effects are most pronounced when the slit width or obstacle size is comparable to the wavelength of the wave; if it is much larger, diffraction is negligible.

Multiple choice

25.In single-slit diffraction, the condition for the positions of the dark fringes (minima) for a slit of width a is:

  • Aa sinθ = (n + 1/2)λ
  • Ba sinθ = λ/2 only
  • Ca cosθ = nλ
  • Da sinθ = nλ, n = 1, 2, 3, ...

Answer: D

For single-slit diffraction, minima (dark fringes) occur at angles θ satisfying a sinθ = nλ, where n = 1, 2, 3, ... (n ≠ 0).

Multiple choice

26.Compared to the secondary maxima, the central maximum in a single-slit diffraction pattern is:

  • AAbsent altogether
  • BNarrower and dimmer
  • CThe same width but dimmer
  • DWider and brighter

Answer: D

The central maximum in single-slit diffraction is about twice as wide as each secondary maximum and is significantly more intense (brightest part of the pattern).

Multiple choice

27.If the width of a single slit is decreased (wavelength constant), the central diffraction maximum on the screen:

  • AStays exactly the same width
  • BDisappears completely
  • CBecomes wider
  • DBecomes narrower

Answer: C

Since the angular position of the first minimum satisfies sinθ = λ/a, decreasing the slit width a increases θ, spreading the central maximum wider.

Multiple choice

28.A single slit of width 0.2 mm is illuminated with light of wavelength 500 nm. Find the angle to the first diffraction minimum.

  • A14.3°
  • B0.0143°
  • C0.143°
  • D1.43°

Answer: C

sinθ = λ/a = (500×10⁻⁹)/(0.2×10⁻³) = 2.5 × 10⁻³ rad. θ ≈ 0.143° (since sinθ ≈ θ in radians for small angles).

Multiple choice

29.The key distinction between interference and diffraction is that:

  • ADiffraction requires two separate light sources, while interference requires only one
  • BInterference only occurs with sound waves, while diffraction only occurs with light
  • CThere is no real physical difference between the two phenomena
  • DInterference involves the superposition of waves from two or more coherent sources, while diffraction involves the spreading and superposition of secondary wavelets from a single wavefront/aperture

Answer: D

Interference is typically described as superposition of waves from two (or more) distinct coherent sources, whereas diffraction results from the superposition of secondary wavelets originating from different points across a single wavefront or aperture.

Multiple choice

30.Young's double-slit experiment is historically significant because it:

  • AProvided strong evidence for the wave nature of light by demonstrating interference
  • BShowed that light cannot diffract
  • CProved that light travels only in straight lines
  • DDisproved the existence of the electromagnetic spectrum

Answer: A

By producing a clear interference pattern of bright and dark fringes, Young's experiment provided strong evidence that light behaves as a wave, contradicting the purely corpuscular (particle) theory of light of the time.

True or false

31.Electromagnetic waves require a material medium in order to propagate.

Answer: False

Electromagnetic waves consist of oscillating electric and magnetic fields and can travel through a vacuum; they do not require a medium, unlike mechanical waves.

True or false

32.For a stable interference pattern to be observed, the two light sources must be coherent, having the same frequency and a constant phase difference.

Answer: True

Coherence (same frequency, constant phase relationship) is essential; without it, the interference pattern shifts too rapidly to be observed and the light appears uniformly bright.

True or false

33.In Young's double-slit experiment, the fringe width is independent of the wavelength of light used.

Answer: False

Fringe width β = λD/d is directly proportional to the wavelength λ, so changing the wavelength changes the fringe spacing.

True or false

34.In single-slit diffraction, the central maximum is the brightest and widest part of the pattern.

Answer: True

The central maximum receives the greatest constructive contribution from the wavelets across the slit and spans roughly twice the angular width of each secondary maximum.

True or false

35.Destructive interference occurs when the path difference between two coherent waves equals an odd multiple of half the wavelength.

Answer: True

At path differences of (n + 1/2)λ, the two waves arrive exactly out of phase and cancel, producing a dark fringe (destructive interference).

Fill in the blank

36.Electromagnetic waves consist of oscillating ______ and magnetic fields that are perpendicular to each other and to the direction of wave travel.

Answer: electric

An electromagnetic wave has mutually perpendicular oscillating electric and magnetic field components, both perpendicular to the direction of propagation.

Fill in the blank

37.The fringe spacing in Young's double-slit experiment is given by the formula β = ______.

Answer: λD/d

Fringe width β equals λD/d, where λ is the wavelength, D the slit-to-screen distance, and d the slit separation.

Fill in the blank

38.Two sources that emit waves of the same frequency with a constant phase difference are called ______ sources.

Answer: coherent

Coherent sources are required to produce a stable, observable interference pattern.

Fill in the blank

39.In single-slit diffraction, dark fringes (minima) occur when a sinθ = ______, where a is the slit width.

Answer: nλ

The minima in a single-slit diffraction pattern occur at angles satisfying a sinθ = nλ, for n = 1, 2, 3, ...

Fill in the blank

40.The bending and spreading of light waves as they pass through a narrow slit or around an obstacle is called ______.

Answer: diffraction

Diffraction is most noticeable when the slit width or obstacle size is comparable to the wavelength of the light.

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