Question 1
Topic: 1.4 Scalars and vectors.png)
The table shows some physical quantities.
Which row correctly identifies the quantities as scalars or vectors?
| acceleration | charge | kinetic energy | wavelength | |
|---|---|---|---|---|
| A | scalar | vector | vector | scalar |
| B | vector | vector | scalar | scalar |
| C | scalar | scalar | scalar | vector |
| D | vector | scalar | scalar | scalar |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Acceleration is a vector quantity because it has both magnitude and direction.
Charge, kinetic energy and wavelength are scalar quantities because they have magnitude only.
Therefore, the correct answer is (D).
Question 2
Topic: 1.3 Errors and uncertainties
Two quantities are measured.
\( L = 6.8 \pm 0.1\,\mathrm{cm} \)
\( T = 2.42 \pm 0.08\,\mathrm{s} \)
\( L \) and \( T \) are related to \( X \) by the equation
\( X=\dfrac{4\pi^{2}L}{T^{2}} \)
What is the calculated value and uncertainty of \( X \)?
(B) \( 45.8 \pm 0.3\,\mathrm{cm\,s^{-2}} \)
(C) \( 46 \pm 2\,\mathrm{cm\,s^{-2}} \)
(D) \( 46 \pm 4\,\mathrm{cm\,s^{-2}} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The calculated value is
\( X=\dfrac{4\pi^{2}(6.8)}{(2.42)^{2}}\approx 45.8\,\mathrm{cm\,s^{-2}} \), which rounds to \( 46\,\mathrm{cm\,s^{-2}} \).
For multiplication and division, percentage uncertainties are added:
\( \dfrac{\Delta X}{X}=\dfrac{\Delta L}{L}+2\left(\dfrac{\Delta T}{T}\right)=\dfrac{0.1}{6.8}+2\left(\dfrac{0.08}{2.42}\right)\approx0.081 \).
Absolute uncertainty \( \approx 0.081\times45.8\approx3.7\,\mathrm{cm\,s^{-2}} \), which rounds to \( \pm4\,\mathrm{cm\,s^{-2}} \).
Therefore, the correct answer is (D).
Question 3
Topic: 1.2 SI units.png)
What are the SI base units of the watt?
(B) \( \mathrm{kg\,m^{2}\,s^{-3}} \)
(C) \( \mathrm{kg\,m^{2}\,s^{-1}} \)
(D) \( \mathrm{N\,m\,s^{-1}} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Power is defined as energy transferred per unit time:
\( \mathrm{W = \dfrac{J}{s}} \).
Since \( \mathrm{J = kg\,m^{2}\,s^{-2}} \), the SI base units of the watt are
\( \mathrm{kg\,m^{2}\,s^{-3}} \).
Therefore, the correct answer is (B).
Question 4
Topic: 1.4 Scalars and vectors
The diagram shows two forces of \( 6.0\,\mathrm{N} \) acting on an object. The angle between the lines of action of the two forces is \( 60^\circ \).
What is the magnitude of the resultant force?
(B) \( 7.9\,\mathrm{N} \)
(C) \( 10\,\mathrm{N} \)
(D) \( 12\,\mathrm{N} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Using the cosine rule for vector addition,
\( R=\sqrt{F_1^2+F_2^2+2F_1F_2\cos\theta} \).
Substituting \( F_1=F_2=6.0\,\mathrm{N} \) and \( \theta=60^\circ \),
\( R=\sqrt{6^2+6^2+2(6)(6)\cos60^\circ}=\sqrt{36+36+36}=\sqrt{108}\approx10.4\,\mathrm{N} \).
To two significant figures, the resultant force is \( 10\,\mathrm{N} \).
Therefore, the correct answer is (C).
Question 5
Topic: 2.1 Equations of motion.png)
A goods train passes through a station at a constant speed of \( 10\,\mathrm{m\,s^{-1}} \) at time \( t=0 \). An express train is at rest at the station. The express train leaves the station with a uniform acceleration of \( 0.5\,\mathrm{m\,s^{-2}} \) just as the goods train goes past. Both trains move in the same direction on straight, parallel tracks.
At which time \( t \) does the express train overtake the goods train?
(B) \( 10\,\mathrm{s} \)
(C) \( 20\,\mathrm{s} \)
(D) \( 40\,\mathrm{s} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The goods train travels with constant speed, so its displacement is
\( s_{\mathrm{goods}}=10t \).
The express train starts from rest with uniform acceleration, so its displacement is
\( s_{\mathrm{express}}=\dfrac{1}{2}at^2=\dfrac{1}{2}(0.5)t^2=0.25t^2 \).
At the instant the trains are together,
\( 0.25t^2=10t \).
Hence \( t=40\,\mathrm{s} \) (ignoring the trivial solution \( t=0 \)).
Therefore, the correct answer is (D).
Question 6
Topic: 2.1 Equations of motion
A ball is held above the ground and released. It falls to the ground and bounces several times.
The graph shows the variation with time \( t \) of the velocity \( v \) of the ball.
Four points on the graph are labelled \( P \), \( Q \), \( R \) and \( S \).
Which statement is not correct?
(B) The collisions of the ball with the ground are inelastic.
(C) The gradient of the line \( RS \) represents the acceleration due to free fall.
(D) The maximum upwards velocity of the ball is reached at point \( P \).
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The area under the velocity-time graph \( PQ \) gives the distance fallen, which is the initial height of the ball.
Each bounce reduces the magnitude of the upward velocity, showing that kinetic energy is lost during each collision. Hence the collisions are inelastic.
The straight-line section \( RS \) has a constant gradient equal to the acceleration due to gravity.
Point \( P \) corresponds to the ball being released from rest, so its velocity is zero. The maximum upward velocity occurs immediately after a bounce, not at \( P \).
Therefore, the correct answer is (D).
Question 7
Topic: 2.1 Equations of motion.png)
An object is projected horizontally. The object falls a vertical distance \( y \) and travels a horizontal distance \( x \) before landing on the ground.
A second object is projected horizontally with the same initial velocity and falls a vertical distance \( 4y \) before landing on the ground.
Assume that air resistance is negligible.
Which horizontal distance does the second object travel?
(B) \( 2x \)
(C) \( 4x \)
(D) \( 16x \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
For horizontal projection, the vertical motion is given by
\( y=\dfrac{1}{2}gt^2 \).
If the vertical distance becomes \( 4y \), then
\( 4y=\dfrac{1}{2}gt_2^2 \Rightarrow t_2=2t \).
The horizontal distance is
\( x=ut \).
Since the horizontal speed \( u \) is unchanged, doubling the time doubles the horizontal distance.
Hence the second object travels \( 2x \).
Therefore, the correct answer is (B).
Question 8
Topic: 3.2 Non-uniform motion.png)
A sphere falls from rest through the air. The graph shows the variation with time of the sphere’s velocity.
Which diagram shows the forces acting on the sphere when it is at the velocity corresponding to point \( P \) on the graph?
(B) Only the weight acts on the sphere.
(C) Weight is greater than air resistance.
(D) Air resistance is greater than the weight.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
At point \( P \), the sphere is still accelerating downward because the velocity-time graph has a positive gradient.
This means the resultant force is downward, so the weight must be greater than the air resistance.
As the sphere continues to fall, the air resistance increases until it becomes equal to the weight at terminal velocity.
Therefore, the correct answer is (C).
Question 9
Topic: 3.3 Linear momentum and its conservation
In which situation is total linear momentum always conserved?
(B) In collisions between two objects moving at equal and opposite velocity.
(C) In collisions between two objects that form an isolated system.
(D) In collisions between two objects with the same mass.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The total linear momentum of a system remains constant only when no external resultant force acts on the system.
Such a system is called an isolated system.
The masses of the objects or their initial velocities do not guarantee conservation of momentum if external forces are present.
Therefore, the correct answer is (C).
Question 10
Topic: 3.3 Linear momentum and its conservation
An object of mass \( m \) moving with velocity \( 9.0\,\mathrm{m\,s^{-1}} \) has a head-on elastic collision with a stationary object of mass \( 2m \).
After the collision, both objects are moving. No external forces act on the system.
What is the velocity of the object of mass \( 2m \) after the collision?
(B) \( -3.0\,\mathrm{m\,s^{-1}} \)
(C) \( 4.5\,\mathrm{m\,s^{-1}} \)
(D) \( 6.0\,\mathrm{m\,s^{-1}} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
For a one-dimensional elastic collision, the final velocity of the second object is
\( v_2=\dfrac{2m_1}{m_1+m_2}u_1 \).
Substituting \( m_1=m \), \( m_2=2m \), \( u_1=9.0\,\mathrm{m\,s^{-1}} \), and \( u_2=0 \),
\( v_2=\dfrac{2m}{3m}\times9.0=6.0\,\mathrm{m\,s^{-1}} \).
Therefore, the correct answer is (D).
Question 11
Topic: 3.1 Momentum and Newton’s laws of motion.png)
The graph shows how the momentum of a motorcycle changes with time.
What is the resultant force on the motorcycle?
(B) \( 5000\,\mathrm{N} \)
(C) \( 25\,000\,\mathrm{N} \)
(D) \( 50\,000\,\mathrm{N} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
The resultant force is the rate of change of momentum:
\( F=\dfrac{\Delta p}{\Delta t} \).
From the graph, the momentum increases from \( 0 \) to \( 5000\,\mathrm{kg\,m\,s^{-1}} \) in \( 10\,\mathrm{s} \).
Hence,
\( F=\dfrac{5000}{10}=500\,\mathrm{N} \).
Therefore, the correct answer is (A).
Question 12
Topic: 3.1 Momentum and Newton’s laws of motion
A rocket has a weight of \( W \) and an initial acceleration of \( a \) as the rocket leaves the ground vertically. The acceleration due to free fall is \( g \).
Which expression gives the initial upward force exerted on the rocket due to the engine?
(B) \( \dfrac{Wa}{g} \)
(C) \( \dfrac{Wa}{g}-W \)
(D) \( Wa+W \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
The mass of the rocket is
\( m=\dfrac{W}{g} \).
Applying Newton’s second law,
\( F-W=ma \).
Substituting \( m=\dfrac{W}{g} \),
\( F=W+\dfrac{Wa}{g} \).
Therefore, the correct answer is (A).
Question 13
Topic: 4.1 Turning effects of forces
A uniform rod of weight \( 28\,\mathrm{N} \) is supported at one end by force \( F \). The rod is in equilibrium and attached to a frictionless hinge at end \( X \).
What is the magnitude of \( F \)?
(B) \( 11\,\mathrm{N} \)
(C) \( 18\,\mathrm{N} \)
(D) \( 21\,\mathrm{N} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Take moments about the hinge at \( X \).
The force \( F \) acts perpendicular to the rod, so its moment is \( FL \), where \( L \) is the length of the rod.
The weight acts at the centre of the rod. Its perpendicular distance from the hinge is
\( \dfrac{L}{2}\cos40^\circ \).
For equilibrium,
\( FL=28\left(\dfrac{L}{2}\right)\cos40^\circ \).
Hence,
\( F=14\cos40^\circ\approx10.7\,\mathrm{N}\approx11\,\mathrm{N} \).
Therefore, the correct answer is (B).
Question 14
Topic: 4.1 Turning effects of forces.png)
Two forces, each of magnitude \( F \), act in opposite directions on a rod.
Each force acts on the rod at a distance \( d \) from the pivot \( P \).
What is the torque of this couple about \( P \)?
(B) \( F\times d \)
(C) \( 2F\times d \)
(D) \( 2F\times2d \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Each force produces a moment of magnitude \( Fd \) about the pivot.
Both moments act in the same rotational direction, so they add together.
Hence, the total torque is
\( \tau=Fd+Fd=2Fd \).
Therefore, the correct answer is (C).
Question 15
Topic: 4.3 Density and pressure
A man of weight \( 600\,\mathrm{N} \) stands with both feet flat on the ground.
What is a reasonable estimate of the pressure exerted on the ground by the weight of the man?
(B) \( 1\times10^{2}\,\mathrm{Pa} \)
(C) \( 1\times10^{4}\,\mathrm{Pa} \)
(D) \( 1\times10^{6}\,\mathrm{Pa} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Pressure is given by
\( P=\dfrac{F}{A} \).
Taking the total contact area of both feet to be approximately \( 0.06\,\mathrm{m^2} \),
\( P\approx\dfrac{600}{0.06}=1.0\times10^{4}\,\mathrm{Pa} \).
This is the closest reasonable estimate.
Therefore, the correct answer is (C).
Question 16
Topic: 4.3 Density and pressure
The formula for the upthrust on a block of wood partially submerged in water is shown.
\( F=\rho gV \)
What do the symbols \( \rho \) and \( V \) represent?
| \( \rho \) | \( V \) | |
|---|---|---|
| A | density of water | volume of whole block |
| B | density of water | volume of block below surface of water |
| C | density of wood | volume of whole block |
| D | density of wood | volume of block below surface of water |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The upthrust equals the weight of the displaced fluid.
In the expression \( F=\rho gV \), \( \rho \) is the density of the fluid (water), and \( V \) is the volume of water displaced, which is equal to the volume of the block below the water surface.
Therefore, the correct answer is (B).
Question 17
Topic: 5.2 Gravitational potential energy and kinetic energy
An object with a mass of \( 100\,\mathrm{g} \) falls a vertical distance of \( 10\,\mathrm{m} \).
What is the change in the gravitational potential energy of the object?
(B) \( 10\,\mathrm{J} \)
(C) \( 100\,\mathrm{J} \)
(D) \( 10\,000\,\mathrm{J} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The change in gravitational potential energy is
\( \Delta E_p=mgh \).
Converting the mass to SI units, \( 100\,\mathrm{g}=0.10\,\mathrm{kg} \).
Hence,
\( \Delta E_p=0.10\times9.8\times10=9.8\,\mathrm{J}\approx10\,\mathrm{J} \).
Therefore, the correct answer is (B).
Question 18
Topic: 5.1 Energy conservation.png)
A bungee jumper jumps from a platform and is decelerated by an elastic bungee cord, as shown.
When the jumper makes the jump, his initial gravitational potential energy relative to the ground is converted into his kinetic energy and into elastic potential energy in the cord.
At which part of the jump are all three types of energy non-zero?
(B) On the way down before the cord has started to extend.
(C) On the way down as he decelerates.
(D) At the bottom of the jump when he is stationary.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
As the jumper decelerates, the cord is stretched so elastic potential energy is stored.
The jumper is still above the ground, so gravitational potential energy is non-zero.
He is also still moving, so his kinetic energy is non-zero.
Therefore, all three forms of energy are present only while he is descending and the cord is stretching.
Therefore, the correct answer is (C).
Question 19
Topic: 5.2 Gravitational potential energy and kinetic energy
A sailboat is pushed by the wind at a constant velocity \( v \) across a lake.
The force of the wind and the velocity of the sailboat are in the same direction.
Which additional information is required to determine the work done per unit time by the wind acting on the sailboat?
(B) The distance travelled by the sailboat per unit time.
(C) The total energy input to the sailboat by the wind.
(D) The weight of the sailboat.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Work done per unit time is the power delivered by the wind.
Since the force and velocity are in the same direction,
\( P=Fv \).
The velocity \( v \) is already given, so the additional information required is the force exerted by the wind.
Therefore, the correct answer is (A).
Question 20
Topic: 6.1 Stress and strain.png)
A spring is fixed at one end. The length \( L \) of the spring is increased by applying a tensile force \( F \) to the other end.
The graph shows the variation of \( L \) with \( F \).
What is the elastic potential energy of the spring when \( F=6.0\,\mathrm{N} \)?
(B) \( 0.24\,\mathrm{J} \)
(C) \( 0.36\,\mathrm{J} \)
(D) \( 0.60\,\mathrm{J} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
From the graph, the spring extends from \( 8\,\mathrm{cm} \) to \( 12\,\mathrm{cm} \), so the extension is
\( x=4\,\mathrm{cm}=0.04\,\mathrm{m} \).
The elastic potential energy is
\( E=\dfrac{1}{2}Fx=\dfrac{1}{2}\times6.0\times0.04=0.12\,\mathrm{J} \).
Therefore, the correct answer is (A).
Question 21
Topic: 6.1 Stress and strain
A wire has an unstretched length of \( 2.00\,\mathrm{m} \).
A stress of \( 1.6\times10^{5}\,\mathrm{Pa} \) is applied to the wire, and the new length of the wire is \( 2.10\,\mathrm{m} \).
The wire obeys Hooke’s law.
What is the Young modulus of the wire?
(B) \( 7.8\times10^{4}\,\mathrm{Pa} \)
(C) \( 1.5\times10^{5}\,\mathrm{Pa} \)
(D) \( 3.2\times10^{6}\,\mathrm{Pa} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Young modulus is
\( E=\dfrac{\text{stress}}{\text{strain}} \).
The strain is
\( \dfrac{\Delta L}{L}=\dfrac{2.10-2.00}{2.00}=0.05 \).
Hence,
\( E=\dfrac{1.6\times10^{5}}{0.05}=3.2\times10^{6}\,\mathrm{Pa} \).
Therefore, the correct answer is (D).
Question 22
Topic: 6.1 Stress and strain
What are the SI base units of stress?
(B) \( \mathrm{kg\,m^{-1}\,s^{-2}} \)
(C) \( \mathrm{kg\,m^{-2}\,s^{-2}} \)
(D) \( \mathrm{kg\,m^{-3}\,s^{-2}} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Stress is force per unit area:
\( \mathrm{stress}=\dfrac{F}{A} \).
Since \( \mathrm{N=kg\,m\,s^{-2}} \),
\( \mathrm{Pa}=\dfrac{\mathrm{N}}{\mathrm{m^2}}=\mathrm{kg\,m^{-1}\,s^{-2}} \).
Therefore, the correct answer is (B).
Question 23
Topic: 6.2 Elastic and plastic behaviour.png)
The diagram shows a force-extension graph for a rubber band as the band is extended and then the stretching force is decreased to zero.
What can be deduced from the graph?
(B) The rubber band obeys Hooke’s law for the extensions shown.
(C) The rubber band remains elastic for the extensions shown.
(D) The shaded area represents the work done in extending the rubber band.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The graph shows hysteresis, so the loading and unloading paths are different. This means the rubber band does not obey Hooke’s law.
The band returns to zero extension when the force is removed, so it remains elastic.
The shaded area represents the energy dissipated during a loading-unloading cycle, not the total work done in extending the band.
Therefore, the correct answer is (C).
Question 24
Topic: 7.1 Progressive waves
Which row is correct for sound waves?
| can travel in a vacuum | can be polarised | can diffract through a gap | |
|---|---|---|---|
| A | no | no | yes |
| B | yes | no | no |
| C | no | yes | no |
| D | no | yes | yes |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Sound waves are mechanical waves and require a material medium, so they cannot travel in a vacuum.
Sound waves are longitudinal and cannot be polarised.
Like all waves, sound waves can diffract when passing through a gap or around an obstacle.
Therefore, the correct answer is (A).
Question 25
Topic: 7.1 Progressive waves.png)
A source emits a progressive sound wave in the horizontal direction. The wave travels away from the source towards the right.
The graph shows the variation of the displacement of the particles from their equilibrium positions with distance from the source at a particular instant in time. Displacements to the right of the equilibrium positions are shown as positive.
Position \( Y \) represents the displacement of a particle in the sound wave at a particular distance from the source at this instant.
Which statement about the motion of this particle is correct?
(B) The particle is moving towards the source.
(C) The particle is moving upwards.
(D) The particle is moving downwards.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Sound is a longitudinal wave, so particles oscillate parallel to the direction of wave travel.
For a wave travelling to the right, the particle velocity is opposite to the slope of the displacement-distance graph.
At point \( Y \), the graph has a positive slope, so the particle is moving towards the source (to the left).
Therefore, the correct answer is (B).
Question 26
Topic: 7.5 Polarisation
Two polarising filters are placed next to each other so that their planes are parallel.
The first polarising filter has its transmission axis at an angle of \( 50^\circ \) to the vertical.
The second polarising filter has its transmission axis at an angle of \( 20^\circ \) to the vertical. The angle between the transmission axes of the two polarising filters is \( 30^\circ \).
A beam of vertically polarised light of intensity \( 8.0\,\mathrm{W\,m^{-2}} \) is incident normally on the first polarising filter.
What is the intensity of the light that is transmitted from the second polarising filter?
(B) \( 2.5\,\mathrm{W\,m^{-2}} \)
(C) \( 2.9\,\mathrm{W\,m^{-2}} \)
(D) \( 6.0\,\mathrm{W\,m^{-2}} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Using Malus’ law for the first filter,
\( I_1=I_0\cos^2 50^\circ=8.0\cos^2 50^\circ\approx3.31\,\mathrm{W\,m^{-2}} \).
The angle between the two transmission axes is \( 30^\circ \), so after the second filter,
\( I_2=I_1\cos^2 30^\circ=3.31\times\frac{3}{4}\approx2.48\,\mathrm{W\,m^{-2}} \).
Hence the transmitted intensity is approximately \( 2.5\,\mathrm{W\,m^{-2}} \).
Therefore, the correct answer is (B).
Question 27
Topic: 7.3 Doppler effect for sound waves
A dolphin is swimming at a speed of \( 16.0\,\mathrm{m\,s^{-1}} \) directly towards a stationary underwater microphone.
The dolphin emits a sound of frequency \( 122\,\mathrm{kHz} \). The speed of sound in water is \( 1480\,\mathrm{m\,s^{-1}} \).
What is the frequency of sound detected by the microphone?
(B) \( 1330\,\mathrm{Hz} \)
(C) \( 121\,\mathrm{kHz} \)
(D) \( 123\,\mathrm{kHz} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
For a source moving towards a stationary observer, the Doppler equation is
\( f’ = f\left(\dfrac{v}{v-v_s}\right) \).
Substituting \( f=122\,\mathrm{kHz} \), \( v=1480\,\mathrm{m\,s^{-1}} \), and \( v_s=16.0\,\mathrm{m\,s^{-1}} \),
\( f’ = 122\left(\dfrac{1480}{1480-16}\right)\approx122\left(\dfrac{1480}{1464}\right)\approx123.3\,\mathrm{kHz} \).
To three significant figures, the detected frequency is \( 123\,\mathrm{kHz} \).
Therefore, the correct answer is (D).
Question 28
Topic: 8.3 Interference.png)
A student carries out a double-slit experiment using a laser emitting red light of wavelength \( 680\,\mathrm{nm} \). The light is incident normally on a double slit.
The diagram shows part of the pattern of bright fringes visible on a screen at a distance of \( 2.4\,\mathrm{m} \) from the slits. The distance across five bright fringes is measured as \( 34\,\mathrm{mm} \).
What is the slit separation?
(B) \( 2.4\times10^{-4}\,\mathrm{m} \)
(C) \( 1.9\times10^{-4}\,\mathrm{m} \)
(D) \( 4.8\times10^{-5}\,\mathrm{m} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The fringe spacing is
\( w=\dfrac{34\,\mathrm{mm}}{4}=8.5\times10^{-3}\,\mathrm{m} \).
Using the double-slit equation
\( w=\dfrac{\lambda D}{d} \), so
\( d=\dfrac{\lambda D}{w}=\dfrac{(680\times10^{-9})(2.4)}{8.5\times10^{-3}}\approx1.9\times10^{-4}\,\mathrm{m} \).
Therefore, the correct answer is (C).
Question 29
Topic: 8.1 Stationary waves
The diagram shows a stationary wave on a stretched spring at an instant in time.
Two particles on the spring, \( P \) and \( Q \), are shown.
Which statement about the vibrations of \( P \) and \( Q \) is correct?
(B) They have the same amplitudes.
(C) They have different periods.
(D) They are always in phase.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Points \( P \) and \( Q \) lie between the same pair of nodes, so they are in the same loop of the stationary wave.
All particles within the same loop oscillate in phase, although their amplitudes may differ depending on their positions.
They also have the same frequency and period.
Therefore, the correct answer is (D).
Question 30
Topic: 8.4 The diffraction grating
Green laser light passes through a diffraction grating and forms an interference pattern.
The diffraction grating contains \( 400 \) lines per \( \mathrm{mm} \).
The wavelength of the laser light is \( 550\,\mathrm{nm} \).
What is the highest order diffraction maximum produced by the grating?
(B) \( 5 \)
(C) \( 8 \)
(D) \( 9 \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
The grating spacing is
\( d=\dfrac{1}{400\times10^{3}}=2.5\times10^{-6}\,\mathrm{m} \).
The highest possible order satisfies
\( n\lambda\le d \).
Hence,
\( n\le\dfrac{2.5\times10^{-6}}{550\times10^{-9}}\approx4.55 \).
The greatest integer value is \( n=4 \).
Therefore, the correct answer is (A).
Question 31
Topic: 9.2 Potential difference and power
There is a potential difference \( V \) across a resistor of resistance \( R \). The current in the resistor is \( I \).
Which equation gives the power dissipated by the resistor?
(B) \( P=\dfrac{V^{2}}{I} \)
(C) \( P=V^{2}R \)
(D) \( P=\dfrac{V^{2}}{R} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Electrical power is given by
\( P=VI \).
Using Ohm’s law, \( I=\dfrac{V}{R} \).
Substituting into the power equation,
\( P=V\left(\dfrac{V}{R}\right)=\dfrac{V^{2}}{R} \).
Therefore, the correct answer is (D).
Question 32
Topic: 11.2 Fundamental particles.png)
What is a possible charge on a particle?
(B) \( 4.00\times10^{-19}\,\mathrm{C} \)
(C) \( 1.12\times10^{-18}\,\mathrm{C} \)
(D) \( 9.11\times10^{-18}\,\mathrm{C} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Electric charge is quantised and must be an integer multiple of the elementary charge,
\( e=1.60\times10^{-19}\,\mathrm{C} \).
\( 1.12\times10^{-18}\,\mathrm{C}=7\times1.60\times10^{-19}\,\mathrm{C} \), which is an integer multiple of \( e \).
The other values are not whole-number multiples of the elementary charge.
Therefore, the correct answer is (C).
Question 33
Topic: 9.3 Resistance and resistivity
The graphs show possible current-voltage (\( I\!-\!V \)) characteristics for a filament lamp and for a semiconductor diode.
Which row identifies the \( I\!-\!V \) graphs for the lamp and for the diode?
| filament lamp | semiconductor diode | |
|---|---|---|
| A | P | R |
| B | P | S |
| C | Q | R |
| D | Q | S |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
A filament lamp has a decreasing gradient on its \( I\!-\!V \) graph because its resistance increases as its temperature rises. This corresponds to graph \( P \).
A semiconductor diode conducts very little current until a threshold voltage is reached, after which the current increases rapidly. This corresponds to graph \( R \).
Therefore, the correct answer is (A).
Question 34
Topic: 10.1 Practical circuits.png)
The diagram shows a circuit containing a battery and cells with negligible internal resistance.
Some values of current, electromotive force (e.m.f.) and resistance are shown.
One resistor is labelled \( P \).
What is the resistance of resistor \( P \)?
(B) \( 0.80\,\Omega \)
(C) \( 2.0\,\Omega \)
(D) \( 2.8\,\Omega \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
At the top junction, \( 3.0\,\mathrm{A} \) enters and \( 2.0\,\mathrm{A} \) leaves through the right-hand branch.
Hence, the current through resistor \( P \) is
\( I_P=3.0+2.0=5.0\,\mathrm{A} \).
The \( 2.0\,\Omega \) resistor has a potential difference of
\( V=IR=3.0\times2.0=6.0\,\mathrm{V} \).
Applying Kirchhoff’s loop rule to the left-hand loop,
\( 9.0=6.0+1.0+V_P \), so \( V_P=2.0\,\mathrm{V} \).
Therefore,
\( R_P=\dfrac{V_P}{I_P}=\dfrac{2.0}{5.0}=0.40\,\Omega \).
Therefore, the correct answer is (A).
Question 35
Topic: 10.1 Practical circuits
The diagram shows a circuit with a battery connected to a resistor \( R \). The battery has an internal resistance represented by \( r \).
A second resistor, identical to \( R \), is connected in parallel with \( R \).
Which row describes the changes to the potential difference (p.d.) across \( r \) and the current shown on the ammeter when the second resistor is connected?
| p.d. across \( r \) | current shown on ammeter | |
|---|---|---|
| A | decreases | decreases |
| B | decreases | increases |
| C | increases | decreases |
| D | increases | increases |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Adding a second identical resistor in parallel reduces the external resistance of the circuit.
The total current drawn from the battery therefore increases.
The p.d. across the internal resistance is \( V_r=Ir \). Since the current increases and \( r \) is constant, the p.d. across \( r \) also increases.
Hence both the p.d. across \( r \) and the ammeter reading increase.
Therefore, the correct answer is (D).
Question 36
Topic: 9.3 Resistance and resistivity.png)
Two identical wires \( X \) and \( Y \), each of length \( L \) and radius \( r \), are connected in parallel as shown.
The total resistance of this combination is \( R_1 \).
Wire \( X \) is replaced with a wire of the same material with length \( L \) and radius \( 2r \).
The total resistance of the new combination is \( R_2 \).
What is the ratio \( \dfrac{R_1}{R_2} \)?
(B) \( \dfrac{2}{3} \)
(C) \( \dfrac{3}{2} \)
(D) \( \dfrac{5}{2} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Initially, each wire has resistance \( R \), so
\( R_1=\dfrac{R}{2} \).
Since \( R=\dfrac{\rho L}{A} \), doubling the radius makes the area four times larger, so the new resistance of wire \( X \) is \( \dfrac{R}{4} \).
The new parallel resistance is
\( R_2=\dfrac{\left(\dfrac{R}{4}\right)R}{\dfrac{R}{4}+R}=\dfrac{R}{5} \).
Hence,
\( \dfrac{R_1}{R_2}=\dfrac{R/2}{R/5}=\dfrac{5}{2} \).
Therefore, the correct answer is (D).
Question 37
Topic: 10.2 Kirchhoff’s laws
The diagram shows the currents in part of an electric circuit.
The resistors are identical.
Which equation is not correct?
(B) \( I_2=I_1-I_3 \)
(C) \( I_2=I_3+I_4+I_5 \)
(D) \( I_4=I_3-I_5 \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Applying Kirchhoff’s current law at the lower junction gives
\( I_3=I_4+I_5 \).
At the upper junction,
\( I_1=I_2+I_3 \).
Hence, \( I_2=I_1-I_3 \), and since \( I_3=I_4+I_5 \), option (A) is also correct.
Option (C) incorrectly states \( I_2=I_3+I_4+I_5 \), which does not satisfy Kirchhoff’s current law.
Therefore, the correct answer is (C).
Question 38
Topic: 11.1 Atoms, nuclei and radiation
The diagram shows a sequence of radioactive decays involving three \( \alpha \)-particles and one \( \beta^- \) particle.
What is nuclide \( T \)?
(B) \( ^{233}_{88}\mathrm{Ra} \)
(C) \( ^{225}_{90}\mathrm{Th} \)
(D) \( ^{229}_{90}\mathrm{Th} \)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Starting with \( ^{237}_{93}\mathrm{Np} \):
Each \( \alpha \)-decay decreases the mass number by \( 4 \) and the proton number by \( 2 \).
One \( \beta^- \)-decay increases the proton number by \( 1 \) but leaves the mass number unchanged.
After three \( \alpha \)-decays and one \( \beta^- \)-decay:
Mass number \( =237-12=225 \).
Proton number \( =93-6+1=88 \).
Hence, \( T=^{225}_{88}\mathrm{Ra} \).
Therefore, the correct answer is (A).
Question 39
Topic: 11.2 Fundamental particles.png)
The number of electrons in a neutral atom of an isotope of plutonium, \( ^{239}_{94}\mathrm{Pu} \), is changed to produce a charged atom (ion) \( W \).
\( W \) has an overall charge of \( +1.6\times10^{-19}\,\mathrm{C} \).
How many protons, neutrons and electrons are in \( W \)?
| protons | neutrons | electrons | |
|---|---|---|---|
| A | 94 | 145 | 93 |
| B | 94 | 145 | 95 |
| C | 238 | 94 | 239 |
| D | 239 | 94 | 238 |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Plutonium has atomic number \( 94 \), so it contains \( 94 \) protons.
The number of neutrons is
\( 239-94=145 \).
A charge of \( +1.6\times10^{-19}\,\mathrm{C} \) is equal to \( +e \), meaning one electron has been removed.
Hence the ion has \( 93 \) electrons.
Therefore, the correct answer is (A).
Question 40
Topic: 11.2 Fundamental particles
Which particle is a lepton?
(B) positron
(C) proton
(D) quark
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Leptons are fundamental particles that do not experience the strong nuclear interaction.
The positron is the antiparticle of the electron and is classified as a lepton.
A meson is made of a quark and an antiquark, a proton is a baryon made of three quarks, and a quark is not itself a lepton.
Therefore, the correct answer is (B).