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.
1.Which of the following correctly defines simple harmonic motion (SHM)?
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.
2.In SHM, the amplitude is best described as:
Answer: A
Amplitude (A) is the maximum displacement from the equilibrium (mean) position.
3.The period (T) and frequency (f) of an oscillation are related by:
Answer: B
Frequency is the reciprocal of the period: f = 1/T, so T = 1/f.
4.In the equation x = A cos(ωt + φ), the quantity φ represents the:
Answer: D
φ is the phase constant, which fixes the state (position and direction of motion) of the oscillator at t = 0.
5.Which of the following is the best real-life example of (approximately) simple harmonic motion?
Answer: D
For small angular displacements, a simple pendulum's restoring force is approximately proportional to displacement, giving SHM.
6.In x = A cos(ωt + φ), the symbol ω represents the:
Answer: A
ω is the angular frequency, related to frequency by ω = 2πf, with units rad/s.
7.A particle in SHM has amplitude 0.05 m and period 2 s. What is its maximum speed?
Answer: D
ω = 2π/T = 2π/2 = π rad/s. v_max = Aω = 0.05 × π ≈ 0.157 m/s.
8.A particle executing SHM has angular frequency 4 rad/s. When its displacement is 0.02 m from equilibrium, its acceleration is:
Answer: B
a = -ω²x = -(4)²(0.02) = -0.32 m/s²; the negative sign shows it is directed towards equilibrium.
9.For a particle in SHM, the displacement–time graph is a cosine curve. The corresponding acceleration–time graph is:
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.
10.In SHM, the velocity–time graph is out of phase with the displacement–time graph by:
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.
11.In SHM, at the equilibrium position (x = 0), the kinetic energy of the oscillator is:
Answer: D
At x = 0 the speed is maximum (v_max = Aω), so kinetic energy is maximum there, while potential energy is zero.
12.In SHM, the potential energy of the oscillator is maximum when:
Answer: A
At the extremes x = ±A, velocity is zero and all the mechanical energy is stored as potential energy.
13.The total mechanical energy of an undamped SHM oscillator, E = ½mω²A², is:
Answer: D
In the absence of damping, mechanical energy continuously converts between kinetic and potential forms but the total remains constant.
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:
Answer: C
E = ½mω²A² = 0.5 × 0.2 × 5² × 0.1² = 0.5 × 0.2 × 25 × 0.01 = 0.025 J.
15.For an SHM oscillator of amplitude A, the kinetic energy when the displacement is x = A/2 is:
Answer: A
KE = ½mω²(A²-x²) = ½mω²(A² - A²/4) = (3/4)(½mω²A²) = 3/4 of the total energy E.
16.The period of a simple pendulum of length l at a place with gravitational acceleration g is given by:
Answer: B
The standard formula for the period of a simple pendulum (small oscillations) is T = 2π√(l/g).
17.If the length of a simple pendulum is quadrupled while g stays constant, its period will:
Answer: D
Since T ∝ √l, quadrupling l multiplies T by √4 = 2, so the period doubles.
18.A simple pendulum is taken to the Moon, where g is smaller than on Earth. Its period will:
Answer: A
Since T = 2π√(l/g), a smaller g gives a larger T, so the period increases on the Moon.
19.The period of a mass–spring system with spring constant k and mass m is:
Answer: C
For a mass-spring oscillator, T = 2π√(m/k), derived from ω = √(k/m) and T = 2π/ω.
20.If the spring constant of a mass–spring system is made 4 times larger while the mass is unchanged, the period becomes:
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.
21.A mass-spring system has period 2 s and mass 0.5 kg. Its spring constant is approximately:
Answer: C
k = 4π²m/T² = 4π²(0.5)/(2²) = 4π²(0.5)/4 = π²(0.5) ≈ 4.93 N/m.
22.For small oscillations, the period of a simple pendulum depends on:
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.
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:
Answer: A
This property — equal periods regardless of (small) amplitude — is called isochronism.
24.The relationship between angular frequency ω and frequency f is:
Answer: B
Angular frequency ω = 2πf, since one full cycle (2π rad) corresponds to one period T = 1/f.
25.A vibrating object has frequency 50 Hz. Its angular frequency is approximately:
Answer: C
ω = 2πf = 2π × 50 ≈ 314.16 rad/s.
26.In x = A cos(ωt + φ), the quantity (ωt + φ) is called the:
Answer: D
(ωt + φ) is the phase of the oscillation; it determines the exact state (position and direction) of the oscillator at time t.
27.The restoring force in SHM is given by F = -kx. The negative sign shows that the force is:
Answer: B
The negative sign indicates the restoring force always acts opposite to the displacement, pulling the particle back to equilibrium.
28.A particle in SHM has amplitude 0.1 m and frequency 2 Hz. Its maximum acceleration is approximately:
Answer: C
ω = 2πf = 2π(2) ≈ 12.57 rad/s. a_max = ω²A = (12.57)² × 0.1 ≈ 15.8 m/s².
29.The graph of acceleration (a) against displacement (x) for an SHM oscillator is:
Answer: A
Since a = -ω²x, a plotted against x gives a straight line through the origin with slope -ω².
30.Which of the following is NOT an example of (approximate) simple harmonic motion?
Answer: C
A ball rolling down an incline undergoes uniformly accelerated, non-oscillatory motion, so it is not SHM.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
1.A damped oscillation is best described as one in which:
Answer: B
Damping is caused by resistive forces (friction, air resistance, viscosity) that remove energy from the system, so the amplitude decays with time.
2.Which of the following is a real-life example of a damped oscillation?
Answer: A
A car suspension oscillates and its amplitude dies away due to resistive (damping) forces from the shock absorber fluid.
3.In a damped oscillator, the damping (resistive) force is generally modelled as being proportional to the object's:
Answer: D
Damping forces (such as viscous drag) are typically proportional to velocity, F = -bv, where b is the damping coefficient.
4.The differential equation describing a damped oscillator of mass m, damping coefficient b, and spring constant k is:
Answer: D
The damped oscillator equation includes an inertial term, a damping term proportional to velocity, and a restoring term proportional to displacement.
5.For a lightly (under-) damped oscillator, the solution to the equation of motion has the general form:
Answer: B
Underdamped motion oscillates at a slightly reduced angular frequency ω' while its amplitude decays exponentially as e^{-bt/2m}.
6.Which type of damping allows a displaced system to return to equilibrium in the shortest possible time without oscillating at all?
Answer: A
Critical damping is the boundary case where the system returns to equilibrium as fast as possible without oscillating back and forth.
7.An overdamped system, when displaced and released, will:
Answer: B
In overdamping, resistive forces are so large that the system creeps back to equilibrium slowly and monotonically, without oscillating.
8.In an underdamped (lightly damped) system, the displaced object:
Answer: B
Underdamping is characterised by repeated oscillations whose amplitude decays exponentially with time until the system comes to rest.
9.Which of the following is a good real-life example of a system deliberately designed to be critically (or near-critically) damped?
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.
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:
Answer: A
A very stiff closer that prevents any oscillation but closes sluggishly is exhibiting overdamped behaviour.
11.In forced oscillations, once steady state is reached, the oscillating system vibrates at:
Answer: D
After transients die away, a forced oscillator settles into vibrating at the same frequency as the periodic driving force applied to it.
12.Resonance in a forced oscillating system occurs when:
Answer: D
Resonance occurs when the frequency of the applied periodic force matches the system's own natural frequency, producing maximum amplitude.
13.At resonance, the amplitude of a forced oscillator is:
Answer: A
The amplitude–frequency response of a forced oscillator peaks sharply at (or near) the natural frequency, giving maximum amplitude at resonance.
14.Regarding energy in a forced oscillation at steady state, which statement is correct?
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.
15.The collapse of the Tacoma Narrows Bridge in 1940 is often cited as a dramatic real-life example of:
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.
16.In musical instruments such as a guitar, the hollow wooden body amplifies the sound of the vibrating string mainly because of:
Answer: C
The body/air cavity has natural frequencies that resonate with the string's vibrations, reinforcing and amplifying the sound produced.
17.Soldiers marching across a bridge are traditionally ordered to break step. This is done to avoid:
Answer: D
If the soldiers' marching frequency matched the bridge's natural frequency, resonance could build up dangerously large oscillations.
18.Increasing the amount of damping in a forced oscillating system generally has what effect on the resonance peak?
Answer: A
More damping removes energy faster, reducing the maximum amplitude reached at resonance and broadening the frequency response curve.
19.For a damped oscillator, which quantity decreases exponentially with time (while damped oscillation continues)?
Answer: C
In underdamped motion the amplitude envelope decays as A0 e^{-bt/2m}, while the angular frequency and period change only slightly.
20.Compared with the natural (undamped) angular frequency ω0, the angular frequency ω' of a lightly damped oscillator is:
Answer: D
Light damping slightly reduces the oscillation frequency: ω' = √(ω0² - (b/2m)²), which is a little less than ω0.
21.In the damping equation m(d²x/dt²) + b(dx/dt) + kx = 0, the constant b represents the:
Answer: A
b is the damping coefficient, quantifying how strongly the resistive force opposes the motion.
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?
Answer: B
Shock absorbers aim for near-critical damping: enough to quickly kill oscillations from bumps without making the ride harsh and sluggish.
23.As the degree of light damping in an oscillator increases (while it remains underdamped), the period of oscillation:
Answer: B
Since ω' = √(ω0² - (b/2m)²) decreases as damping (b) increases, and T' = 2π/ω', the period slightly increases with more damping.
24.The mechanical energy of a freely (unforced) damped oscillator, over time, will:
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.
25.Which displacement–time graph best represents an underdamped oscillation?
Answer: C
Underdamped motion continues to oscillate about equilibrium, but with the peak amplitude shrinking exponentially over successive cycles.
26.Compared to overdamping, critical damping brings a displaced system back to equilibrium:
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.
27.A pneumatic door closer adjusted so the door closes slowly and gently, without slamming or swinging back open, is behaving as a(n):
Answer: A
A door that creeps closed slowly with no oscillation, taking longer than the minimum possible time, is exhibiting overdamped behaviour.
28.The natural (resonant) frequency of a simple mass–spring oscillator mainly depends on:
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.
29.Which of these is NOT a genuine real-life example of resonance?
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.
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:
Answer: B
0.5 = e^{-4λ} ⟹ ln(0.5) = -4λ ⟹ λ = ln2/4 ≈ 0.693/4 ≈ 0.173 s⁻¹.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
1.A mechanical wave is best defined as a wave that:
Answer: B
Unlike electromagnetic waves, mechanical waves need a material medium — such as air, water, or a solid — to transmit their energy.
2.In a transverse wave, the particles of the medium vibrate:
Answer: C
In transverse waves (e.g. waves on a stretched string), particle displacement is at right angles to the direction the wave travels.
3.In a longitudinal wave, the particles of the medium vibrate:
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.
4.Which of the following is the best example of a longitudinal mechanical wave?
Answer: B
Sound waves involve air particles oscillating back and forth along the direction of propagation, making them longitudinal waves.
5.For a progressive wave given by y = A sin(ωt - kx), the quantity k is called the:
Answer: D
k is the wave number (or propagation constant), related to wavelength λ by k = 2π/λ.
6.A progressive sound wave has frequency 256 Hz and wavelength 1.3 m. Its speed is approximately:
Answer: B
Using v = fλ: v = 256 × 1.3 ≈ 332.8 m/s, close to the typical speed of sound in air.
7.A wave has wavelength 0.5 m. Its wave number k is approximately:
Answer: A
k = 2π/λ = 2π/0.5 ≈ 12.57 rad/m.
8.A wave has a frequency of 100 Hz. Its angular frequency ω is approximately:
Answer: C
ω = 2πf = 2π × 100 ≈ 628.3 rad/s.
9.In the wave equation y = A sin(ωt - kx), the constant A represents the:
Answer: D
A is the amplitude — the maximum displacement of a particle from its equilibrium position as the wave passes.
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:
Answer: C
Phase difference between two points a distance Δx apart is Δφ = kΔx, where k is the wave number.
11.A distinguishing feature of a progressive (travelling) wave is that it:
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.
12.A stationary (standing) wave is formed when:
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.
13.Which of the following best represents the equation of a stationary wave formed on a string?
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.
14.In a stationary wave, points that remain permanently at rest (zero displacement at all times) are called:
Answer: C
Nodes are the fixed points of zero amplitude in a standing wave pattern.
15.In a stationary wave, points of maximum amplitude of vibration are called:
Answer: A
Antinodes are the points where the standing wave amplitude is greatest.
16.The distance between two adjacent nodes in a stationary wave is:
Answer: A
Adjacent nodes in a standing wave pattern are separated by half a wavelength, λ/2.
17.The distance between a node and the nearest adjacent antinode in a stationary wave is:
Answer: A
A node and its neighbouring antinode are always a quarter wavelength (λ/4) apart.
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:
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.
19.For a string of length L and wave speed v fixed at both ends, the fundamental frequency is given by:
Answer: A
Since λ1 = 2L for the fundamental mode, f1 = v/λ1 = v/(2L).
20.A string of length 0.6 m has wave speed 300 m/s along it. Its fundamental frequency of vibration is:
Answer: B
f1 = v/(2L) = 300/(2 × 0.6) = 300/1.2 = 250 Hz.
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:
Answer: A
The second harmonic has one extra node compared to the fundamental, fitting a full wavelength into the string, so λ2 = L.
22.Regarding energy transfer, a stationary wave differs from a progressive wave in that a stationary wave:
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.
23.Which of the following is a good real-life example of a stationary (standing) wave?
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.
24.Which of the following is a good real-life example of a progressive (travelling) wave?
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.
25.For the wave equation y = A sin(ωt - kx), the negative sign before kx indicates that the wave travels:
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.
26.The wave speed (v), wavelength (λ) and period (T) of a progressive wave are related by:
Answer: C
Since the wave moves one wavelength in one period, its speed is v = λ/T (equivalently v = fλ).
27.Sound waves travelling through air are classified as:
Answer: B
Sound propagates through air via alternating compressions and rarefactions, with particle motion parallel to the direction of travel — a longitudinal wave.
28.Regarding water surface waves, which statement is most accurate?
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.
29.A progressive wave is described by y = 0.02 sin(4πt - 2πx) (SI units). The speed of this wave is:
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.
30.A wave in air has frequency 50 Hz and travels at the speed of sound, 340 m/s. Its wavelength is:
Answer: A
λ = v/f = 340/50 = 6.8 m.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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:
Answer: A
The pressure due to a liquid column is P = hρg, which increases linearly with depth h and with density ρ.
2.Using g = 10 m/s², the pressure at a depth of 10 m in water (density 1000 kg/m³) is:
Answer: C
P = hρg = 10 × 1000 × 10 = 100,000 Pa = 1 × 10⁵ Pa.
3.Pascal's principle states that:
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.
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:
Answer: C
Pressure is transmitted equally: F1/A1 = F2/A2 ⟹ F2 = F1 × (A2/A1) = 50 × (0.1/0.001) = 5,000 N.
5.The rise (or fall) of a liquid in a narrow tube due to surface tension effects is called:
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.
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:
Answer: D
The standard capillary rise formula is h = 2Tcosθ/(rρg).
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:
Answer: C
Since h ∝ 1/r, a narrower tube produces a greater capillary rise.
8.Capillary depression (the liquid surface being pushed down in a narrow tube) occurs typically when:
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.
9.The SI unit of surface tension is:
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).
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:
Answer: B
The Reynolds number is defined as Re = ρvd/η, a dimensionless number comparing inertial to viscous forces in the flow.
11.A low Reynolds number for fluid flow in a pipe generally indicates:
Answer: D
Low Reynolds numbers correspond to viscous forces dominating over inertial forces, favouring smooth, orderly laminar flow.
12.A high Reynolds number for fluid flow generally indicates:
Answer: C
At high Reynolds numbers, inertial forces dominate, and small disturbances grow into chaotic eddies, producing turbulent flow.
13.The continuity equation A1v1 = A2v2 for an incompressible fluid expresses the principle of:
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.
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:
Answer: C
By continuity, A1v1 = A2v2 ⟹ v2 = (A1v1)/A2 = (0.02 × 3)/0.01 = 6 m/s.
15.Bernoulli's equation, P + ½ρv² + ρgh = constant, along a streamline represents:
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.
16.According to Bernoulli's principle, in a horizontal flow where the fluid speed increases, the pressure of the fluid:
Answer: D
For horizontal flow, P + ½ρv² = constant, so an increase in speed v must be accompanied by a decrease in pressure P.
17.The lift on an aircraft wing is commonly explained using Bernoulli's principle by noting that:
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.
18.A perfume atomizer (spray bottle) works by using a rapid stream of air blown across the top of a narrow tube, which:
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.
19.In a carburettor, a narrow constriction (venturi) in the air passage is used to:
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.
20.A laboratory filter pump (aspirator) removes air from a flask using:
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.
21.Sailing boats can make progress even when sailing partly against the wind mainly because:
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.
22.Terminal velocity of an object falling through a viscous fluid is reached when:
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.
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:
Answer: A
Stokes' law gives the terminal velocity of a small sphere in a viscous fluid as v_t = 2r²g(ρ - σ)/(9η).
24.At the instant an object reaches terminal velocity while falling through a fluid, its acceleration is:
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.
25.The velocity–time graph of an object released from rest and falling through a viscous fluid typically shows:
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.
26.The SI unit of dynamic viscosity (η) is:
Answer: D
Dynamic viscosity has SI units of pascal-seconds (Pa·s), equivalent to N·s/m².
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:
Answer: C
Since v_t = 2r²g(ρ-σ)/(9η), terminal velocity is inversely proportional to viscosity η, so increasing η decreases v_t.
28.If the radius of a falling sphere is doubled while everything else stays the same, its terminal velocity (by Stokes' law) becomes:
Answer: B
Since v_t ∝ r², doubling the radius increases the terminal velocity by a factor of 2² = 4.
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:
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.
30.Which of the following does NOT directly affect the height of capillary rise in a tube, according to h = 2Tcosθ/(rρg)?
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
1.Newton's law of universal gravitation states that the gravitational force between two point masses is
Answer: D
F = Gm1m2/r², so F is proportional to m1m2 and inversely proportional to r².
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.
3.Two point masses of 1000 kg and 500 kg have their centres 2.0 m apart. What is the gravitational force between them?
Answer: D
F = Gm1m2/r² = (6.67×10⁻¹¹ × 1000 × 500)/2² = (3.335×10⁻⁵)/4 = 8.34×10⁻⁶ N.
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.
5.If the distance between two masses is doubled while the masses stay constant, the gravitational force between them
Answer: D
F is proportional to 1/r², so doubling r reduces F by a factor of 2² = 4.
6.Gravitational field strength at a point is defined as
Answer: B
Field strength g = F/m, the force per unit mass placed at the point, measured in N/kg.
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.
8.The gravitational field strength at a distance r from a point mass M is given by
Answer: A
Combining F = GMm/r² with g = F/m gives g = GM/r².
9.In a diagram of a gravitational field around an isolated spherical mass, the field lines
Answer: D
Gravitational field lines always point in the direction a small test mass would be pulled, i.e. towards the source mass.
10.Which of the following is NOT a typical effect of the Earth's gravitational field?
Answer: C
Movement of charge between conductors is an electrical effect, not gravitational; weight, orbits and tides are all gravitational effects.
11.How does the acceleration due to gravity, g, vary with height h above the Earth's surface (radius R, surface value g₀)?
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.
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
Answer: B
g = g₀R²/(2R)² = g₀R²/4R² = g₀/4.
13.Assuming the Earth has uniform density, how does g vary with depth d below the surface (radius R)?
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.
14.At a depth equal to half the Earth's radius (assuming uniform density), the value of g is
Answer: D
g = g₀(1 − d/R) = g₀(1 − 0.5) = g₀/2.
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).
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.
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).
18.A mountaineer climbs to the top of a high mountain. Compared to sea level, their weight at the summit is
Answer: C
Increasing r decreases g = GM/r², so the gravitational force (weight) is slightly smaller at altitude, even though mass is unchanged.
19.Deep in a mine shaft below the Earth's surface, the value of g compared to its surface value is
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).
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
Answer: A
GMm/r² = mv²/r leads to v² = GM/r, so v = √(GM/r).
21.For a satellite in circular orbit, Kepler's third law relates the orbital period T and orbital radius r as
Answer: C
From GMm/r² = m(4π²/T²)r, we get T² = 4π²r³/GM, i.e. T² ∝ r³.
22.The time period of a satellite in a circular orbit of radius r about the Earth (mass M) is given by
Answer: A
Derived from T² = 4π²r³/(GM): T = 2π√(r³/GM).
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.
24.A geostationary satellite is one that
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.
25.For a satellite to be geostationary, it must orbit
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.
26.The approximate altitude of a geostationary satellite above the Earth's surface is
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.
27.Geostationary satellites are especially useful for
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.
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.
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.
Answer: A
v = √(GM/r) = √((6.67×10⁻¹¹ × 6.0×10²⁴)/7.0×10⁶) = √(5.72×10⁷) ≈ 7.6×10³ m/s.
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
Answer: C
T² ∝ r³, so TB/TA = (rB/rA)^(3/2) = 4^(3/2) = 8.
31.The escape velocity from a planet of mass M and radius R is given by
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).
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.
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.
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.
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
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.
35.Which statement about the direction of the gravitational field of a uniform spherical mass is correct?
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.
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.
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
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.
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.
39.A key assumption used to derive g = g₀(1 − d/R) for the variation of gravity with depth is that
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.
40.If Earth's mass were to suddenly double while its radius stayed the same, the surface value of g would
Answer: D
g = GM/R²; if M doubles and R is unchanged, g doubles proportionally.
1.Thomson's 'plum pudding' model of the atom described the atom as
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.
2.The alpha-particle scattering experiment that led to Rutherford's nuclear model was performed by
Answer: C
Geiger and Marsden fired alpha particles at thin gold foil under Rutherford's supervision; the results overturned Thomson's model.
3.In the gold foil experiment, most alpha particles passed straight through the foil with little deflection. This suggested that
Answer: C
Since the vast majority of alpha particles passed through undeflected, most of the volume of an atom must be empty space.
4.A small fraction of alpha particles in Rutherford's experiment were deflected through very large angles, some almost straight back. This showed that
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.
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.
6.In Rutherford's nuclear model of the atom, most of the atom's mass is concentrated in
Answer: C
Rutherford's model places almost all the mass and all the positive charge in a very small central nucleus.
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.
8.A major weakness of Rutherford's classical nuclear model was that it could not explain
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.
9.Bohr's model improved on Rutherford's model by proposing that
Answer: B
Bohr postulated quantised, stable orbits (stationary states) in which electrons do not radiate energy, resolving the stability problem of Rutherford's model.
10.According to Bohr's model, an atom emits a photon of light when
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.
11.The energy of a photon emitted or absorbed during an electron transition between two atomic energy levels E1 and E2 is given by
Answer: A
By conservation of energy, the photon's energy hf exactly equals the magnitude of the energy difference between the two levels.
12.Atomic energy levels are described as 'quantised' because
Answer: D
Quantisation means only discrete energy values are allowed for a bound electron, in contrast to a classical continuous range.
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.
14.An electron in an atom that has absorbed energy and moved to a higher energy level is said to be in a(n)
Answer: B
When an electron gains energy and jumps to a higher allowed level, the atom is said to be excited.
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
Answer: D
En = −13.6/n² eV; for n = 2, E2 = −13.6/4 = −3.4 eV.
16.Using En = −13.6/n² eV for hydrogen, the energy needed to ionise a hydrogen atom from its ground state (n = 1) is
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.
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
Answer: B
ΔE = E3 − E2 = −1.51 − (−3.4) = 1.89 eV, which is released as a photon.
18.The set of spectral lines produced by hydrogen electron transitions ending at n = 1 is known as the
Answer: D
Transitions ending on the n = 1 (ground) level produce the Lyman series, which lies in the ultraviolet region.
19.The Balmer series of hydrogen spectral lines corresponds to electron transitions that end at
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.
20.Which spectral series of hydrogen lies mainly in the visible region of the electromagnetic spectrum?
Answer: C
The Balmer series (transitions ending at n = 2) produces lines with wavelengths in the visible range, historically the first hydrogen series discovered.
21.The Paschen series of hydrogen spectral lines results from transitions ending at
Answer: C
The Paschen series consists of transitions from higher levels down to n = 3, and lies in the infrared region.
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.
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.
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
Answer: B
The Rydberg constant is approximately R = 1.097 × 10⁷ m⁻¹, used to calculate hydrogen spectral line wavelengths.
25.Emission line spectra are produced when
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.
26.Absorption spectra appear as
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.
27.One important application of atomic spectral analysis is
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.
28.Thermionic emission is the process by which
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.
29.The work function of a metal is defined as
Answer: A
Work function φ is the minimum energy required to liberate an electron from a metal's surface into the surrounding vacuum.
30.Which of the following factors increases the rate of thermionic emission from a metal filament?
Answer: D
Thermionic emission increases strongly with temperature, since more electrons gain enough thermal energy to exceed the work function as temperature rises.
31.A metal with a lower work function will, at the same temperature, generally show
Answer: A
A lower work function means less energy is needed for electrons to escape, so more electrons are emitted at a given temperature.
32.Which of the following is NOT typically listed as a factor affecting the rate of thermionic emission?
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).
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.
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.
35.An applied electric field near a heated metal surface can increase thermionic emission by
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.
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.
37.Bohr's model successfully explained the line spectrum of which atom, matching experimental spectral line wavelengths closely?
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.
38.A vacuum diode uses thermionic emission from a heated cathode; the emitted electrons are then accelerated toward the
Answer: A
Electrons emitted from the heated cathode are attracted to and collected by the positively charged anode, producing current flow through the tube.
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 = ∞.
40.Compared to Rutherford's classical model, Bohr's key new assumption was that
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.
1.A blackbody is best described as an object that
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.
2.The Stefan-Boltzmann law for the total power radiated by a blackbody is given by
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.
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).
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
Answer: D
P = σAT⁴ = 5.67×10⁻⁸ × 0.02 × (500)⁴ = 5.67×10⁻⁸ × 0.02 × 6.25×10¹⁰ ≈ 70.9 W.
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.
6.The classical (Rayleigh-Jeans) theory of blackbody radiation failed at short wavelengths, a problem historically known as the
Answer: C
Classical wave theory predicted infinite radiated energy at short (ultraviolet) wavelengths, a clear contradiction with experiment called the ultraviolet catastrophe.
7.Planck resolved the ultraviolet catastrophe by proposing that
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.
8.In Planck's quantum theory, the energy of one quantum of radiation of frequency f is given by
Answer: B
Planck proposed that radiant energy is quantised in units of E = hf, where h is Planck's constant.
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.
10.According to the photon theory of light, a beam of light can be thought of as consisting of
Answer: C
Einstein's photon theory treats light as a stream of discrete energy quanta (photons), each with energy E = hf.
11.Calculate the energy of a photon of light with frequency 6.0 × 10¹⁴ Hz, given h = 6.63 × 10⁻³⁴ J·s.
Answer: B
E = hf = 6.63×10⁻³⁴ × 6.0×10¹⁴ = 3.98×10⁻¹⁹ J.
12.The energy of a photon can also be written in terms of wavelength λ and the speed of light c as
Answer: A
Since c = fλ, substituting f = c/λ into E = hf gives E = hc/λ.
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
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.
14.Wave-particle duality refers to the idea that
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.
15.The principle of complementarity, introduced by Bohr, states that
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.
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.
17.In the photoelectric effect, the threshold frequency is defined as
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.
18.Einstein's photoelectric equation is written as
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.
19.The work function of a metal in the photoelectric effect is
Answer: B
The work function φ represents the minimum energy an electron must gain to escape the metal surface.
20.In a photoelectric experiment, the stopping potential is the
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.
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
Answer: A
KE_max = hf − φ = 4.14 eV − 2.0 eV = 2.14 eV.
22.In the photoelectric effect, increasing the intensity of light (above the threshold frequency) while keeping frequency constant results in
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.
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.
24.If the frequency of incident light on a metal surface is below the threshold frequency, then
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.
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.
26.A photocell has a threshold wavelength of 600 nm. Using hc ≈ 1240 eV·nm, the work function of the metal is approximately
Answer: D
φ = hc/λ₀ = 1240 eV·nm / 600 nm ≈ 2.07 eV.
27.The photoelectric effect provided strong evidence for the
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.
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
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.
29.de Broglie proposed that particles of matter, such as electrons, have an associated wavelength given by
Answer: A
The de Broglie wavelength relates a particle's wave nature to its momentum: λ = h/p = h/(mv).
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
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.
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.
32.Because de Broglie's wavelength λ = h/p is inversely proportional to momentum, macroscopic (large, everyday) objects have de Broglie wavelengths that are
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.
33.Which observation is best explained using the particle (photon) model of light rather than the wave model?
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.
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).
35.As the temperature of a blackbody increases, the wavelength at which it emits most strongly (according to Wien's displacement law)
Answer: C
Wien's displacement law, λ_max T = constant, shows that as temperature increases, the peak emission wavelength shifts to shorter (bluer) wavelengths.
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
Answer: C
P ∝ T⁴, so doubling T multiplies radiated power by 2⁴ = 16, assuming equal surface areas.
37.Which of the following best explains why increasing the intensity of light below the threshold frequency still produces no photoelectrons?
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.
38.The graph of maximum kinetic energy of photoelectrons (KE_max) versus frequency (f) of incident light is a straight line whose gradient represents
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.
39.In the KE_max versus frequency graph for the photoelectric effect, the frequency-axis intercept represents
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.
40.Complementarity in quantum physics is closely linked to which idea?
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.
1.Communication, in the context of physics and engineering, is best defined as
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.
2.Why is communication important in modern society?
Answer: B
Effective communication systems enable fast exchange of information essential for business, education, emergency services, governance and everyday social life.
3.Which of the following is an example of a wired (guided) communication system?
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.
4.Which of the following is an example of a wireless communication system?
Answer: A
Radio broadcasting transmits electromagnetic waves through free space (air) rather than along a physical conductor, making it a wireless system.
5.The three basic components shown in the block diagram of a general communication system are
Answer: D
Every communication system can be represented in block form as: information source → transmitter → channel (medium) → receiver → destination.
6.In a communication system, the function of the transmitter is to
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.
7.The channel in a communication system refers to
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.
8.The function of the receiver in a communication system is to
Answer: C
The receiver detects the incoming signal and processes it (e.g. demodulates, amplifies) to reconstruct the original information for the destination.
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.
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.
11.A signal, in communication systems, is defined as
Answer: B
A signal is a time-varying physical quantity, typically an electrical voltage or current, used to represent and carry information.
12.An analogue signal is one that
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.
13.A digital signal is one that
Answer: A
Digital signals are represented using discrete levels, most commonly binary values of 0 and 1, unlike the continuously varying analogue signal.
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.
15.Which of the following is an example of an analogue signal?
Answer: C
A microphone converts continuously varying sound pressure into a continuously varying voltage, which is an analogue signal.
16.The process of converting a digital signal into an analogue signal is called
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.
17.The process of converting an analogue signal into a digital signal is called
Answer: D
An Analog-to-Digital Converter (ADC) samples a continuous analogue signal and represents it as discrete digital values.
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.
19.Why is signal conversion (ADC/DAC) important in modern communication systems?
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).
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.
21.Modulation, in communication systems, is defined as
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).
22.The main reason a message (baseband) signal is modulated onto a high-frequency carrier before transmission is to
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.
23.In Amplitude Modulation (AM), the property of the carrier wave that is varied according to the information signal is its
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.
24.In Frequency Modulation (FM), the property of the carrier wave that is varied according to the information signal is its
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.
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.
26.Which type of modulation keeps the carrier wave's frequency constant but changes its amplitude to match the message signal?
Answer: D
AM varies carrier amplitude while frequency stays fixed; this is the defining feature that distinguishes it from FM and PM.
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.
28.A radio communication system fundamentally consists of
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).
29.In a radio receiver, the component that extracts the original information signal from the modulated carrier wave is called the
Answer: C
The demodulator (or detector) reverses the modulation process at the receiver, recovering the original message signal from the received modulated carrier.
30.The antenna in a radio communication system is used to
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.
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.
32.The telegraph, an early form of long-distance electrical communication, primarily transmitted messages using
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.
33.Compared to the telegraph, the telephone represented an advance because it allowed
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.
34.A key advantage of digital communication systems over analogue systems is that digital signals
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.
35.Which of the following is an example of a modern digital communication system?
Answer: B
Modern mobile networks convert voice and data into digital form for transmission, offering better noise resistance, security and efficient use of bandwidth.
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.
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.
38.Bandwidth, in the context of communication systems, refers to
Answer: B
Bandwidth is the width of the frequency range that a signal occupies or that a communication channel is able to carry.
39.Compared to AM radio, FM radio generally requires
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.
40.Satellite communication systems are a modern type of communication system that primarily rely on
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.
1.What is a magnetic field?
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.
2.Which of the following is NOT a property of magnetic field lines?
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.
3.Outside a bar magnet, magnetic field lines point:
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.
4.According to the right-hand grip rule, if a straight wire carries current upward, the magnetic field lines around it form:
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.
5.The magnetic field at a perpendicular distance r from a long straight current-carrying wire carrying current I is given by:
Answer: D
The magnetic field around an infinite straight conductor is B = μ₀I/(2πr), decreasing inversely with distance from the wire.
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)
Answer: C
B = μ₀I/(2πr) = (4π×10⁻⁷ × 10)/(2π × 0.05) = (2×10⁻⁶)/(0.05) = 4 × 10⁻⁵ T.
7.The magnetic field inside a long, tightly-wound solenoid carrying current I with n turns per unit length is given by:
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.
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)
Answer: C
n = N/l = 500/0.5 = 1000 turns/m. B = μ₀nI = 4π×10⁻⁷ × 1000 × 2 = 2.51 × 10⁻³ T.
9.Doubling the number of turns per unit length of a solenoid (keeping current constant) causes the magnetic field inside it to:
Answer: D
Since B = μ₀nI, the field is directly proportional to n, so doubling n doubles B.
10.The magnetic field pattern inside a current-carrying solenoid closely resembles the field of:
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.
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:
Answer: B
Magnetic flux is Φ = BA cosθ, where θ is measured between the field direction and the normal (perpendicular) to the surface.
12.Magnetic flux through a loop is maximum when:
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.
13.The SI unit of magnetic flux is the:
Answer: B
Magnetic flux is measured in Weber (Wb), where 1 Wb = 1 T·m².
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:
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.
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.
Answer: A
Since the wire is perpendicular to B, θ = 90°, so F = BIL sinθ = 0.2 × 5 × 0.3 × 1 = 0.3 N.
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:
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.
17.The direction of the force on a current-carrying conductor in a magnetic field is best determined using:
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).
18.The magnetic force on a charge q moving with velocity v at angle θ to a magnetic field B is given by:
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.
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?
Answer: A
F = qvB sinθ = (1.6×10⁻¹⁹)(2×10⁶)(0.5)(sin90°) = 1.6 × 10⁻¹³ N.
20.A charged particle moving parallel to a magnetic field experiences:
Answer: A
Since F = qvB sinθ, when the velocity is parallel to B (θ = 0°), sinθ = 0, so the force is zero.
21.A charged particle moving in a uniform magnetic field, with velocity always perpendicular to B, moves in a:
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).
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.
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.
23.In a simple DC motor, the split-ring commutator serves to:
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.
24.In a DC motor, the carbon brushes function to:
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.
25.The basic structure of a simple DC motor includes all of the following EXCEPT:
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.
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:
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).
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.
Answer: B
Maximum torque: τ = NBIA = 100 × 0.1 × 2 × 0.02 = 0.4 N·m.
28.Increasing the number of turns in the coil of a DC motor (all else constant) will:
Answer: A
Since torque τ = NBIA sinφ, torque is directly proportional to the number of turns N, so increasing N increases the torque.
29.In a DC motor, the permanent (field) magnets are primarily responsible for:
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.
30.A DC motor converts:
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
1.The theory of relativity is primarily concerned with:
Answer: A
Relativity studies how quantities such as time, length, mass, and simultaneity are measured differently by observers in relative motion to one another.
2.An inertial reference frame is one that:
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.
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:
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.
4.In the Galilean transformation, time is assumed to be:
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.
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:
Answer: B
Galilean relativity simply adds velocities: the ground observer sees the ball moving at u + v, since velocities are assumed to combine additively.
6.The first postulate of Einstein's special theory of relativity states that:
Answer: A
Einstein's first postulate (principle of relativity) states that the laws of physics take the same form in every inertial reference frame.
7.The second postulate of Einstein's special theory of relativity states that:
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.
8.Which experimental result motivated Einstein's postulate about the speed of light?
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.
9.One major implication of Einstein's postulates is that:
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.
10.The Lorentz factor γ is defined as:
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.
11.Calculate the Lorentz factor γ for an object moving at v = 0.6c.
Answer: D
γ = 1/√(1 − v²/c²) = 1/√(1 − 0.36) = 1/√0.64 = 1/0.8 = 1.25.
12.Time dilation is described by the equation:
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.
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?
Answer: B
γ = 1.25 for v = 0.6c, so Δt = γΔt₀ = 1.25 × 2 s = 2.5 s.
14.As observed from a stationary (Earth) frame, a clock moving at high speed relative to that frame appears to:
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.
15.Proper time (Δt₀) is defined as the time interval between two events:
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.
16.Length contraction is described by the equation:
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.
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?
Answer: A
γ = 1/√(1 − 0.64) = 1/√0.36 = 1/0.6 ≈ 1.667. L = L₀/γ = 100/1.667 = 60 m.
18.Length contraction occurs:
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.
19.The proper length of an object is:
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.
20.Einstein's mass-energy equivalence relation is expressed as:
Answer: C
Einstein showed that mass and energy are equivalent and related by E = mc², where c is the speed of light in vacuum.
21.Calculate the energy equivalent of a mass of 1 gram (1 × 10⁻³ kg) using E = mc² (c = 3 × 10⁸ m/s).
Answer: C
E = mc² = (1×10⁻³)(3×10⁸)² = (1×10⁻³)(9×10¹⁶) = 9 × 10¹³ J.
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)?
Answer: D
From E = mc², m = E/c² = (1.8×10⁻¹⁰)/(9×10¹⁶) = 2 × 10⁻²⁷ kg.
23.One implication of E = mc² is that:
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.
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:
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.
25.The relativity of simultaneity means that:
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.
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:
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.
27.GPS satellite clocks must be corrected for relativistic effects mainly because:
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.
28.As v increases from 0 toward c, the Lorentz factor γ:
Answer: C
Since γ = 1/√(1 − v²/c²), as v increases toward c, the denominator approaches zero, so γ increases without bound toward infinity.
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:
Answer: D
γ = 1.25 for v = 0.6c. L = L₀/γ = 50/1.25 = 40 m.
30.Which statement correctly compares Galilean and Einsteinian relativity?
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
1.An electromagnetic wave is best described as:
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.
2.Electromagnetic waves can travel through:
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.
3.The speed of electromagnetic waves in a vacuum is approximately:
Answer: B
All electromagnetic waves travel at the speed of light in vacuum, c ≈ 3 × 10⁸ m/s, regardless of their frequency or wavelength.
4.Arranged in order of increasing frequency, the electromagnetic spectrum is:
Answer: A
In order of increasing frequency (decreasing wavelength), the spectrum runs radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, then gamma rays.
5.Which region of the electromagnetic spectrum is commonly used for medical imaging of bones due to its high penetrating power?
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.
6.Microwaves are commonly applied in:
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.
7.For two light sources to produce a sustained (observable) interference pattern, they must be:
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.
8.Constructive interference occurs at points where the path difference between two coherent waves is:
Answer: B
Constructive interference (bright fringes) occurs when the path difference equals a whole number of wavelengths: Δ = nλ, where n = 0, ±1, ±2, ...
9.Destructive interference occurs at points where the path difference between two coherent waves is:
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.
10.Why can't two independent light bulbs produce a stable interference pattern?
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.
11.In Young's double-slit experiment, the two coherent sources are typically obtained by:
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.
12.In Young's double-slit experiment, the fringe spacing (fringe width) β is given by:
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.
13.In a Young's double-slit setup, λ = 600 nm, D = 1 m, and d = 1 mm. Calculate the fringe width.
Answer: C
β = λD/d = (600×10⁻⁹ × 1)/(1×10⁻³) = 6 × 10⁻⁴ m = 0.6 mm.
14.If the slit separation d in Young's double-slit experiment is increased while λ and D stay constant, the fringe width:
Answer: D
Since β = λD/d, fringe width is inversely proportional to slit separation d, so increasing d decreases the fringe width.
15.If the wavelength of light used in Young's double-slit experiment is increased (D and d fixed), the fringe width will:
Answer: C
Since β = λD/d, fringe width is directly proportional to wavelength, so a longer wavelength produces wider fringes.
16.Increasing the distance D between the double slit and the screen, with λ and d constant, causes the fringe width to:
Answer: D
Since β = λD/d, fringe width increases directly with the slit-to-screen distance D.
17.In Young's double-slit pattern, the central bright fringe occurs where:
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).
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:
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, ...
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:
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.
20.According to the intensity distribution of the double-slit fringe pattern, the intensity is zero (dark fringe) when the phase difference φ equals:
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).
21.The relationship between phase difference φ and path difference Δ for two interfering waves of wavelength λ is:
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.
22.Two coherent waves have a path difference of λ/2. What is their phase difference?
Answer: B
φ = (2π/λ)Δ = (2π/λ)(λ/2) = π rad, which corresponds to destructive interference.
23.Diffraction of light refers to:
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.
24.Diffraction effects become most noticeable when the size of the slit or obstacle is:
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.
25.In single-slit diffraction, the condition for the positions of the dark fringes (minima) for a slit of width a is:
Answer: D
For single-slit diffraction, minima (dark fringes) occur at angles θ satisfying a sinθ = nλ, where n = 1, 2, 3, ... (n ≠ 0).
26.Compared to the secondary maxima, the central maximum in a single-slit diffraction pattern is:
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).
27.If the width of a single slit is decreased (wavelength constant), the central diffraction maximum on the screen:
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.
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.
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).
29.The key distinction between interference and diffraction is that:
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.
30.Young's double-slit experiment is historically significant because it:
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.
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.
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.
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.
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.
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).
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.
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.
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.
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, ...
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.