Question 1
Topic: 1.4 Scalars and vectors.png)
Which quantity is a scalar quantity?
(B) momentum
(C) velocity
(D) work
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
A scalar quantity has magnitude only and no direction.
Force, momentum and velocity are vector quantities because they have both magnitude and direction.
Work is a scalar quantity because it has magnitude only.
Therefore, the correct answer is (D).
Question 2
Topic: 1.3 Errors and uncertainties
What is the effect of a systematic error on the measurement of a physical quantity?
(B) It limits the range of values obtained in repeated measurements.
(C) It results in repeated measurements having different values from each other.
(D) It results in the measured value being different from the correct value.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
A systematic error causes every measurement to be shifted by the same amount or by the same proportion in one direction.
This reduces the accuracy of the measurement but does not affect its precision or the spread of repeated readings.
As a result, the measured value differs consistently from the true or correct value.
Therefore, the correct answer is (D).
Question 3
Topic: 3.1 Momentum and Newton’s laws of motion.png)
A car is accelerated by a constant resultant force of \(300\,\mathrm{N}\) for \(5.0\,\mathrm{s}\).
The variation with time of the velocity, in \(\mathrm{cm\,s^{-1}}\), of the car is shown.
What is the mass of the car?
(B) \(1000\,\mathrm{kg}\)
(C) \(1300\,\mathrm{kg}\)
(D) \(10\,000\,\mathrm{kg}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
From the graph, the velocity increases from \(30\,\mathrm{cm\,s^{-1}}\) to \(150\,\mathrm{cm\,s^{-1}}\) in \(5.0\,\mathrm{s}\).
Converting to SI units, \(\Delta v = 120\,\mathrm{cm\,s^{-1}} = 1.2\,\mathrm{m\,s^{-1}}\).
The acceleration is \(a=\dfrac{\Delta v}{t}=\dfrac{1.2}{5.0}=0.24\,\mathrm{m\,s^{-2}}\).
Using \(F=ma\),
\(m=\dfrac{F}{a}=\dfrac{300}{0.24}=1250\,\mathrm{kg}\approx1300\,\mathrm{kg}\).
Therefore, the correct answer is (C).
Question 4
Topic: 2.1 Equations of motion
An aircraft, initially stationary on a runway, takes off with a speed of \(85\,\mathrm{km\,h^{-1}}\) in a distance of no more than \(1.20\,\mathrm{km}\).
What is the minimum constant acceleration necessary for the aircraft?
(B) \(0.46\,\mathrm{m\,s^{-2}}\)
(C) \(3.0\,\mathrm{m\,s^{-2}}\)
(D) \(6.0\,\mathrm{m\,s^{-2}}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Convert the speed to SI units:
\(85\,\mathrm{km\,h^{-1}}=\dfrac{85\times1000}{3600}=23.6\,\mathrm{m\,s^{-1}}\).
Using the equation \(v^2=u^2+2as\), with \(u=0\), \(v=23.6\,\mathrm{m\,s^{-1}}\) and \(s=1200\,\mathrm{m}\),
\(a=\dfrac{v^2}{2s}=\dfrac{(23.6)^2}{2\times1200}\approx0.23\,\mathrm{m\,s^{-2}}\).
This is the minimum constant acceleration needed for the aircraft to reach take-off speed within the given distance.
Therefore, the correct answer is (A).
Question 5
Topic: 2.1 Equations of motion.png)
An object is fired upwards from horizontal ground. The object has an initial velocity of \(20\,\mathrm{m\,s^{-1}}\) at an angle of \(45^\circ\) to the horizontal. Air resistance is negligible.
Which statement describes the speed of the object after it is fired until immediately before it reaches the ground again?
(B) Its speed decreases to a value greater than zero, then increases to a value greater than \(20\,\mathrm{m\,s^{-1}}\).
(C) Its speed decreases to zero, then increases to \(20\,\mathrm{m\,s^{-1}}\).
(D) Its speed decreases to zero, then increases to a value less than \(20\,\mathrm{m\,s^{-1}}\).
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
The horizontal component of velocity remains constant because air resistance is negligible, while the vertical component decreases to zero at the highest point and then increases in the downward direction.
At the highest point, the object still has a horizontal velocity, so its speed is greater than zero.
Since the object lands at the same height from which it was projected and there is no air resistance, its speed immediately before reaching the ground is equal to its initial speed, \(20\,\mathrm{m\,s^{-1}}\).
Therefore, the correct answer is (A).
Question 6
Topic: 3.3 Linear momentum and its conservation
What is a statement of the principle of conservation of momentum for a system?
(B) The total momentum is conserved only in elastic collisions.
(C) The total momentum is conserved provided that no external forces act.
(D) The total momentum of each object in the system is the product of its mass and velocity.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The principle of conservation of momentum states that the total momentum of an isolated system remains constant, provided that no external resultant force acts on the system.
Kinetic energy is conserved only in elastic collisions, so option (A) is incorrect. Momentum is conserved in both elastic and inelastic collisions if there are no external forces, so option (B) is also incorrect.
Option (D) defines the momentum of an individual object, \(p=mv\), rather than stating the conservation principle.
Therefore, the correct answer is (C).
Question 7
Topic: 3.3 Linear momentum and its conservation
Objects P and Q form an isolated system.
Object P has mass \(6.0\,\mathrm{kg}\) and is moving at a speed of \(3.0\,\mathrm{m\,s^{-1}}\).
Object Q has mass \(2.0\,\mathrm{kg}\) and is moving at a speed of \(4.2\,\mathrm{m\,s^{-1}}\) at an angle of \(35^\circ\) to the path of P.
Objects P and Q collide and stick together.
What is the magnitude of the component of the final momentum of the combined objects in the original direction of P?
(B) \(11\,\mathrm{kg\,m\,s^{-1}}\)
(C) \(13\,\mathrm{kg\,m\,s^{-1}}\)
(D) \(25\,\mathrm{kg\,m\,s^{-1}}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Momentum is conserved because the system is isolated.
The momentum of P in its original direction is
\(p_P=6.0\times3.0=18\,\mathrm{kg\,m\,s^{-1}}\).
The component of Q’s momentum in the original direction of P is opposite to P’s motion:
\(p_Q=2.0\times4.2\times\cos35^\circ\approx6.9\,\mathrm{kg\,m\,s^{-1}}\).
Hence, the final momentum component in P’s original direction is
\(18-6.9=11.1\,\mathrm{kg\,m\,s^{-1}}\approx11\,\mathrm{kg\,m\,s^{-1}}\).
Therefore, the correct answer is (B).
Question 8
Topic: 3.1 Momentum and Newton’s laws of motion.png)
An astronaut of mass \(m\) in a spacecraft experiences a gravitational force \(F=mg\) when stationary on the launchpad.
What is the gravitational force on the astronaut when the spacecraft is launched vertically upwards with an acceleration of \(0.2g\)?
(B) \(mg\)
(C) \(0.8mg\)
(D) \(0\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The gravitational force acting on the astronaut is the weight, \(F_g=mg\), which depends only on the astronaut’s mass and the gravitational field strength.
Although the spacecraft accelerates upward, the gravitational force does not change. The upward acceleration increases the normal reaction force (apparent weight), not the gravitational force.
Therefore, the gravitational force on the astronaut remains \(mg\).
Therefore, the correct answer is (B).
Question 9
Topic: 4.1 Turning effects of forces
The diagram shows a child X of mass \(20\,\mathrm{kg}\) and a child Y of mass \(15\,\mathrm{kg}\) seated on a uniform plank.
The plank has a mass of \(7.0\,\mathrm{kg}\) and has a pivot at its midpoint. The plank is horizontal and in equilibrium.
Which statement about the weight of the plank is correct?
(B) The weight of the plank is causing an anticlockwise moment.
(C) The weight of the plank is causing a clockwise moment.
(D) The weight of the plank equals the force on the plank from the pivot.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
A uniform plank has its centre of mass at its midpoint, so its weight acts through the midpoint.
Since the pivot is also at the midpoint, the weight of the plank passes through the pivot and produces no moment.
The force from the pivot supports the combined weight of the plank and both children, not just the weight of the plank.
Therefore, the correct answer is (A).
Question 10
Topic: 4.3 Density and pressure
An object is fully submerged in a liquid.
A student determines the ratio
\(\dfrac{\text{upthrust acting on the object}}{\text{weight of the object}}\).
Which single change would double the value of this ratio?
(B) Use a different object that has half the volume and the same density as the original object.
(C) Use a different object that has twice the density and the same volume as the original object.
(D) Use a different object that has twice the volume and the same density as the original object.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
For a fully submerged object, the upthrust is \(U=\rho_{\mathrm{liquid}}Vg\), while the object’s weight is \(W=\rho_{\mathrm{object}}Vg\).
Hence,
\(\dfrac{U}{W}=\dfrac{\rho_{\mathrm{liquid}}}{\rho_{\mathrm{object}}}\).
Doubling the liquid’s density doubles the ratio, whereas changing only the object’s volume does not affect the ratio because the volume cancels.
Therefore, the correct answer is (A).
Question 11
Topic: 4.2 Equilibrium of forces.png)
A shop sign weighing \(75\,\mathrm{N}\) hangs from a frame attached to a vertical wall.
The frame consists of a horizontal rod \(XY\) and a rod \(YZ\) that is at an angle of \(30^\circ\) to the horizontal. Rod \(XY\) is attached to the wall by a hinge at \(X\) and has length \(0.50\,\mathrm{m}\). Assume that the weights of the rods are negligible.
What is the horizontal force exerted by the wall on rod \(XY\)?
(B) \(43\,\mathrm{N}\)
(C) \(130\,\mathrm{N}\)
(D) \(150\,\mathrm{N}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
At point \(Y\), the vertical component of the tension in rod \(YZ\) balances the weight of the sign:
\(T\sin30^\circ=75\).
Hence, \(T=\dfrac{75}{\sin30^\circ}=150\,\mathrm{N}\).
The horizontal component of this force is
\(T\cos30^\circ=150\times\cos30^\circ\approx130\,\mathrm{N}\).
This is balanced by the horizontal force exerted by the wall on rod \(XY\).
Therefore, the correct answer is (C).
Question 12
Topic: 1.3 Errors and uncertainties
A student takes measurements to calculate the density of a liquid in a beaker.
The height of the liquid in the beaker is \(0.20\,\mathrm{m}\pm2\%\).
The internal diameter of the beaker is \(0.05\,\mathrm{m}\pm3\%\).
The mass of the liquid is \(0.36\,\mathrm{kg}\pm10\%\).
What is the percentage uncertainty in the calculated density of the liquid?
(B) \(5\%\)
(C) \(15\%\)
(D) \(18\%\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The density is
\(\rho=\dfrac{m}{V}=\dfrac{m}{\pi\left(\dfrac{d}{2}\right)^2h}\).
For multiplication and division, percentage uncertainties are added. Since the diameter is squared, its percentage uncertainty is doubled.
Percentage uncertainty in density \(=10\%+2\times3\%+2\%=18\%\).
Therefore, the correct answer is (D).
Question 13
Topic: 4.2 Equilibrium of forces.png)
The diagram shows a uniform plank \(XY\) of length \(4.0\,\mathrm{m}\) and weight \(300\,\mathrm{N}\).
The plank rests on fixed supports at its ends \(X\) and \(Y\).
A child of weight \(600\,\mathrm{N}\) stands in different positions on the plank.
The support at end \(X\) exerts a force \(F\) vertically upwards on the plank.
What is the magnitude of \(F\) when the child stands at \(X\) and when the child stands at \(Y\)?
What is the magnitude of \(F\) when the child stands at \(X\) and when the child stands at \(Y\)?
| \(F\,/\,\mathrm{N}\) when child is at \(X\) | \(F\,/\,\mathrm{N}\) when child is at \(Y\) | |
| (A) | \(600\) | \(0\) |
| (B) | \(600\) | \(150\) |
| (C) | \(750\) | \(0\) |
| (D) | \(750\) | \(150\) |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
The total downward force is \(600+300=900\,\mathrm{N}\).
When the child stands at \(X\), taking moments about \(X\) gives the reaction at \(Y\) as \(150\,\mathrm{N}\). Hence, the reaction at \(X\) is \(900-150=750\,\mathrm{N}\).
When the child stands at \(Y\), taking moments about \(X\) gives the reaction at \(Y\) as \(750\,\mathrm{N}\). Therefore, the reaction at \(X\) is \(900-750=150\,\mathrm{N}\).
Therefore, the correct answer is (D).
Question 14
Topic: 5.2 Gravitational potential energy and kinetic energy
Which relationship is used in the derivation of the equation shown?
\(\text{power}=\text{force}\times\text{velocity}\)
(B) force \(=\) mass \(\times\) acceleration
(C) momentum \(=\) mass \(\times\) velocity
(D) velocity \(=\) acceleration \(\times\) time
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Power is the rate of doing work:
\(P=\dfrac{W}{t}\).
Using \(W=Fs\) and the relationship \(s=vt\),
\(P=\dfrac{Fs}{t}=\dfrac{F(vt)}{t}=Fv\).
Thus, the required relationship is displacement \(=\) velocity \(\times\) time.
Therefore, the correct answer is (A).
Question 15
Topic: 5.1 Energy conservation.png)
A block is released from rest at the top of a slope inclined at an angle to the horizontal. The slope has length \(L\) as shown in the diagram.
There are no resistive forces acting on the block.
What is the speed of the block at the bottom of the slope?
(B) \(4.43\sqrt{L\sin\theta}\)
(C) \(19.6L\cos\theta\)
(D) \(19.6L\sin\theta\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The vertical height descended is
\(h=L\sin\theta\).
Using conservation of mechanical energy,
\(mgh=\dfrac{1}{2}mv^2\).
Hence,
\(v=\sqrt{2gL\sin\theta}=\sqrt{19.6L\sin\theta}=4.43\sqrt{L\sin\theta}\).
Therefore, the correct answer is (B).
Question 16
Topic: 5.1 Energy conservation
A skateboarder and her skateboard have a total mass of \(70\,\mathrm{kg}\). She pushes on the ground with her foot to create a forward force \(F\) of \(25\,\mathrm{N}\) on herself and the skateboard, as shown in the diagram.
The skateboarder and skateboard travel forwards a distance of \(0.50\,\mathrm{m}\) before the skateboarder lifts her foot from the ground.
What is the work done by \(F\) on the skateboarder and skateboard?
(B) \(50\,\mathrm{J}\)
(C) \(340\,\mathrm{J}\)
(D) \(360\,\mathrm{J}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Work done by a constant force is
\(W=Fs\).
Substituting \(F=25\,\mathrm{N}\) and \(s=0.50\,\mathrm{m}\),
\(W=25\times0.50=12.5\,\mathrm{J}\approx13\,\mathrm{J}\).
Therefore, the correct answer is (A).
Question 17
Topic: 5.1 Energy conservation
A turbine at a hydroelectric power station is situated at a vertical distance of \(30\,\mathrm{m}\) below the level of the surface of a large lake. The water passes through the turbine at a rate of \(340\,\mathrm{m^3}\) per minute.
The overall efficiency of the turbine and generator system is \(90\%\). The density of water is \(1000\,\mathrm{kg\,m^{-3}}\).
What is the useful power output of the power station?
(B) \(1.5\,\mathrm{MW}\)
(C) \(1.7\,\mathrm{MW}\)
(D) \(90\,\mathrm{MW}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The volume flow rate is
\(\dfrac{340}{60}=5.67\,\mathrm{m^3\,s^{-1}}\).
The mass flow rate is
\(\dot{m}=1000\times5.67=5.67\times10^3\,\mathrm{kg\,s^{-1}}\).
The useful power is
\(P=\eta\dot{m}gh=0.90\times(5.67\times10^3)\times9.8\times30\approx1.5\times10^6\,\mathrm{W}=1.5\,\mathrm{MW}\).
Therefore, the correct answer is (B).
Question 18
Topic: 5.2 Gravitational potential energy and kinetic energy.png)
A projectile is launched at \(45^\circ\) to the horizontal with initial kinetic energy \(E\).
Assuming air resistance to be negligible, what will be the kinetic energy of the projectile when it reaches its highest point?
(B) \(0.71E\)
(C) \(0.87E\)
(D) \(E\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
At the highest point, the vertical component of velocity is zero, while the horizontal component remains constant.
The horizontal speed is \(v\cos45^\circ=\dfrac{v}{\sqrt{2}}\).
Hence, the kinetic energy at the highest point is
\(\dfrac{1}{2}m\left(\dfrac{v}{\sqrt{2}}\right)^2=\dfrac{1}{4}mv^2=\dfrac{1}{2}E\).
Therefore, the correct answer is (A).
Question 19
Topic: 6.2 Elastic and plastic behaviour
A wire is extended by a tensile force so that its deformation is elastic.
What is meant by elastic deformation?
(B) The extension of the wire is not proportional to the tensile force.
(C) When the tensile force is removed, the wire does not return to its original length.
(D) When the tensile force is removed, the wire returns to its original length.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Elastic deformation is a temporary change in shape or length.
When the applied force is removed, the material regains its original dimensions, provided its elastic limit has not been exceeded.
A proportional relationship between force and extension applies only within the limit of proportionality and is not the definition of elastic deformation.
Therefore, the correct answer is (D).
Question 20
Topic: 6.1 Stress and strain
A bolt is subjected to a tensile force, as shown.
The bolt has a circular cross-section. At end \(X\), the diameter is \(2d\). At end \(Y\), the diameter is \(d\).
What is the ratio
\(\dfrac{\text{stress at }Y}{\text{stress at }X}\) ?
(B) \(0.50\)
(C) \(2.0\)
(D) \(4.0\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Stress is given by
\(\sigma=\dfrac{F}{A}\).
The tensile force is the same throughout the bolt, so the stress is inversely proportional to the cross-sectional area.
Since area is proportional to the square of the diameter,
\(\dfrac{A_X}{A_Y}=\dfrac{(2d)^2}{d^2}=4\).
Hence,
\(\dfrac{\sigma_Y}{\sigma_X}=\dfrac{A_X}{A_Y}=4\).
Therefore, the correct answer is (D).
Question 21
Topic: 6.1 Stress and strain.png)
The graph shows the relationship between force acting on a compression spring and change in length of the spring.
One of these springs is placed in each corner of a horizontal square plate. The axes of each spring are in a vertical direction. These four springs support a total load of \(160\,\mathrm{N}\).
What is the total elastic potential energy stored in the four springs?
(B) \(0.19\,\mathrm{J}\)
(C) \(0.38\,\mathrm{J}\)
(D) \(0.77\,\mathrm{J}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The four springs share the load equally, so each spring supports
\(\dfrac{160}{4}=40\,\mathrm{N}\).
From the graph, a force of \(40\,\mathrm{N}\) compresses each spring by approximately \(2.4\,\mathrm{mm}=2.4\times10^{-3}\,\mathrm{m}\).
The elastic potential energy stored in one spring is
\(E=\dfrac{1}{2}Fx=\dfrac{1}{2}\times40\times2.4\times10^{-3}=0.048\,\mathrm{J}\).
For four springs, the total energy is
\(4\times0.048=0.192\,\mathrm{J}\approx0.19\,\mathrm{J}\).
Therefore, the correct answer is (B).
Question 22
Topic: 7.4 Electromagnetic spectrum.png)
Which row correctly identifies the properties of all electromagnetic waves?
| Transverse wave | Longitudinal wave | Can travel in free space | |
| (A) | ✓ | ✗ | ✓ |
| (B) | ✓ | ✗ | ✗ |
| (C) | ✗ | ✓ | ✓ |
| (D) | ✗ | ✓ | ✗ |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
All electromagnetic waves are transverse waves and can propagate through a vacuum (free space).
They are not longitudinal waves, so only row (A) correctly lists all their properties.
Therefore, the correct answer is (A).
Question 23
Topic: 7.4 Electromagnetic spectrum
What is the approximate range of wavelengths in free space for infrared radiation?
(B) \(300\,\mathrm{\mu m}\) to \(30\,\mathrm{cm}\)
(C) \(400\,\mathrm{nm}\) to \(700\,\mathrm{nm}\)
(D) \(800\,\mathrm{nm}\) to \(1000\,\mathrm{\mu m}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Infrared radiation lies just beyond the red end of the visible spectrum.
Its wavelength range is approximately \(800\,\mathrm{nm}\) to \(1000\,\mathrm{\mu m}\) (or \(1\,\mathrm{mm}\)).
The other ranges correspond to ultraviolet, radio waves, and visible light.
Therefore, the correct answer is (D).
Question 24
Topic: 7.3 Doppler effect for sound waves.png)
The diagram shows a car travelling at a constant speed in a straight line between person P and person Q from point \(X\) to point \(Y\).
The car sounds its horn continuously as it travels. The horn emits sound of constant frequency.
Which statements about what person P and person Q hear during the motion of the car are correct?
1. Person P hears a sound of increasing frequency.
2. Person Q hears a sound of decreasing frequency.
3. Person Q always hears a sound of higher frequency than person P.
(B) 1 and 2 only
(C) 3 only
(D) none of them
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Person P is behind the moving car and hears a lower frequency because the source is moving away, while person Q is in front of the car and hears a higher frequency because the source is approaching.
The frequency heard by each observer remains constant while the car moves at constant speed, so statements 1 and 2 are incorrect.
Person Q always hears a higher frequency than person P, so statement 3 is correct.
Therefore, the correct answer is (C).
Question 25
Topic: 7.1 Progressive waves
A progressive wave of frequency \(300\,\mathrm{Hz}\) is travelling with a speed of \(600\,\mathrm{m\,s^{-1}}\).
What is the phase difference between two points on the wave that are a distance of \(0.50\,\mathrm{m}\) apart?
(B) \(90^\circ\)
(C) \(180^\circ\)
(D) \(360^\circ\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
The wavelength is
\(\lambda=\dfrac{v}{f}=\dfrac{600}{300}=2.0\,\mathrm{m}\).
The phase difference is
\(\phi=\dfrac{0.50}{2.0}\times360^\circ=90^\circ\).
Therefore, the correct answer is (B).
Question 26
Topic: 7.5 Polarisation.png)
A polarised beam of light with intensity \(I\) is incident normally on a polarising filter.
The transmitted light has intensity \(I\).
The filter is rotated about the normal axis through an angle \(\theta\).
The transmitted light has intensity \(0.75I\).
What is the angle \(\theta\)?
(B) \(42^\circ\)
(C) \(49^\circ\)
(D) \(60^\circ\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
Malus’ law states that
\(I=I_0\cos^2\theta\).
Given \(0.75I=I\cos^2\theta\),
\(\cos^2\theta=0.75=\dfrac{3}{4}\).
Hence, \(\cos\theta=\dfrac{\sqrt{3}}{2}\), giving
\(\theta=30^\circ\).
Therefore, the correct answer is (A).
Question 27
Topic: 8.3 Interference
Light waves are emitted from two sources.
What is a necessary condition for observable interference fringes to be produced?
(B) The waves must not be polarised.
(C) The waves must be coherent.
(D) The waves must have equal amplitudes.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Observable interference requires the two sources to be coherent, meaning they maintain a constant phase difference and have the same frequency.
Equal amplitudes are not essential, although they produce higher-contrast fringes. Polarisation is also not a necessary condition.
Therefore, the correct answer is (C).
Question 28
Topic: 8.2 Diffraction
The diagram shows a water wave in a shallow tank. The wave is diffracted through a gap in a barrier and spreads. The wavelength of the wave is much smaller than the width of the gap.
The wavelength of the wave and the width of the gap are both changed by a small amount.
Which combination of changes must increase the amount of spreading due to diffraction?
| Wavelength | Width of gap | |
| (A) | decreases | decreases |
| (B) | decreases | increases |
| (C) | increases | decreases |
| (D) | increases | increases |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The amount of diffraction depends on the ratio of wavelength to gap width.
Diffraction increases when the wavelength becomes larger and/or the gap becomes smaller.
Only option (C) increases the wavelength while decreasing the gap width, guaranteeing greater spreading.
Therefore, the correct answer is (C).
Question 29
Topic: 8.4 The diffraction grating.png)
Light of wavelength \(567\,\mathrm{nm}\) is incident normally on a diffraction grating. The grating has \(400\) lines per \(\mathrm{mm}\). A number of diffraction maxima are observed on the far side of the grating.
What is the angle between the second-order maximum and the third-order maximum?
(B) \(13.9^\circ\)
(C) \(15.9^\circ\)
(D) \(27.0^\circ\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The grating spacing is
\(d=\dfrac{1}{400\times10^3}=2.5\times10^{-6}\,\mathrm{m}\).
Using \(d\sin\theta=n\lambda\):
For \(n=2\), \(\theta_2\approx27.0^\circ\).
For \(n=3\), \(\theta_3\approx42.9^\circ\).
The angle between the maxima is
\(42.9^\circ-27.0^\circ=15.9^\circ\).
Therefore, the correct answer is (C).
Question 30
Topic: 9.1 Electric current
Two cylindrical conductors, \(X\) and \(Y\), are made from the same material. The conductors have equal lengths, but \(Y\) has a smaller diameter than \(X\).
\(X\) and \(Y\) are connected in series to a cell.
Which row compares the number of charge carriers per unit time passing through \(X\) and through \(Y\) and compares the average drift speed of the charge carriers in \(X\) and in \(Y\)?
| Number of charge carriers per unit time | Average drift speed of charge carriers | |
| (A) | Y greater than X | Y greater than X |
| (B) | Y same as X | Y same as X |
| (C) | Y greater than X | Y same as X |
| (D) | Y same as X | Y greater than X |
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
Since the conductors are connected in series, the same current flows through both. Therefore, the number of charge carriers passing a cross-section per unit time is the same.
The drift speed is given by
\(I=nAv_dq\).
As conductor \(Y\) has a smaller cross-sectional area, the drift speed must be greater to maintain the same current.
Therefore, the correct answer is (D).
Question 31
Topic: 9.3 Resistance and resistivity
A copper wire is \(6.4\,\mathrm{m}\) long and has a resistance of \(0.92\,\Omega\).
The resistivity of copper is \(1.8\times10^{-8}\,\Omega\,\mathrm{m}\).
What is the diameter of the wire?
(B) \(1.0\times10^{-4}\,\mathrm{m}\)
(C) \(4.0\times10^{-4}\,\mathrm{m}\)
(D) \(7.1\times10^{-4}\,\mathrm{m}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Using
\(R=\dfrac{\rho L}{A}\),
the cross-sectional area is
\(A=\dfrac{\rho L}{R}=\dfrac{(1.8\times10^{-8})(6.4)}{0.92}=1.25\times10^{-7}\,\mathrm{m^2}\).
Since \(A=\dfrac{\pi d^2}{4}\),
\(d=\sqrt{\dfrac{4A}{\pi}}\approx4.0\times10^{-4}\,\mathrm{m}\).
Therefore, the correct answer is (C).
Question 32
Topic: 9.3 Resistance and resistivity.png)
A thermistor is connected to a cell with negligible internal resistance.
Which graph shows the variation with temperature of power, \(P\), dissipated in the thermistor?
(B) Graph B
(C) Graph C
(D) Graph D
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{A}} \)
For an NTC thermistor, the resistance decreases as the temperature increases.
With a cell of constant voltage, the power dissipated is
\(P=\dfrac{V^2}{R}\).
As \(R\) decreases, the power increases, giving the rising curved graph.
Therefore, the correct answer is (A).
Question 33
Topic: 9.1 Electric current
A metal electrical conductor has a resistance of \(5.6\,\mathrm{k\Omega}\). A potential difference (p.d.) of \(9.0\,\mathrm{V}\) is applied across its ends.
How many electrons pass a point in the conductor in one minute?
(B) \(1.0\times10^{19}\)
(C) \(6.0\times10^{17}\)
(D) \(1.0\times10^{16}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
The current is
\(I=\dfrac{V}{R}=\dfrac{9.0}{5.6\times10^3}=1.61\times10^{-3}\,\mathrm{A}\).
The charge passing in \(60\,\mathrm{s}\) is
\(Q=It=(1.61\times10^{-3})(60)=9.64\times10^{-2}\,\mathrm{C}\).
The number of electrons is
\(N=\dfrac{Q}{e}=\dfrac{9.64\times10^{-2}}{1.60\times10^{-19}}\approx6.0\times10^{17}\).
Therefore, the correct answer is (C).
Question 34
Topic: 9.2 Potential difference and power
Which circuit symbol does not represent an electric component that is designed to emit sound waves?
(B) Symbol B
(C) Symbol C
(D) Symbol D
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Symbols A, C and D represent sound-emitting components such as loudspeakers, buzzers or sounders.
Symbol B represents a resistor, which is not designed to emit sound waves.
Therefore, the correct answer is (B).
Question 35
Topic: 10.1 Practical circuits.png)
The diagram shows a junction in a circuit where three wires, \(P\), \(Q\) and \(R\), meet. The currents in \(P\) and \(Q\) are \(1\,\mathrm{A}\) and \(3\,\mathrm{A}\) respectively, in the directions shown.
How much charge passes a given point in wire \(R\) in a time of \(5\,\mathrm{s}\)?
(B) \(2\,\mathrm{C}\)
(C) \(10\,\mathrm{C}\)
(D) \(20\,\mathrm{C}\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{C}} \)
Using Kirchhoff’s current law, the current entering the junction equals the current leaving the junction.
Current in wire \(R\) is
\(I_R=3-1=2\,\mathrm{A}\).
The charge passing in \(5\,\mathrm{s}\) is
\(Q=It=2\times5=10\,\mathrm{C}\).
Therefore, the correct answer is (C).
Question 36
Topic: 9.2 Potential difference and power
A cell of electromotive force (e.m.f.) \(E\) and internal resistance \(r\) is connected in series with a switch \(S\) and an external resistor of resistance \(R\).
The potential difference (p.d.) between \(P\) and \(Q\) is \(V\).
Which statement is correct when \(S\) is changed from open to closed?
(B) \(V\) decreases because there is a p.d. across \(r\).
(C) \(V\) remains the same because the decrease of p.d. across \(r\) is balanced by the increase of p.d. across \(R\).
(D) \(V\) remains the same because the sum of the p.d.s across \(r\) and \(R\) is still equal to \(E\).
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
With the switch open, no current flows, so the terminal p.d. equals the e.m.f., \(V=E\).
When the switch is closed, current flows through the internal resistance \(r\), producing a voltage drop \(Ir\).
The terminal p.d. becomes
\(V=E-Ir\), which is less than the e.m.f.
Therefore, the correct answer is (B).
Question 37
Topic: 11.2 Fundamental particles
What is a general description of a baryon?
(B) It consists of three quarks that do not need to be the same flavour.
(C) It consists of two quarks that must both be the same flavour.
(D) It consists of two quarks that do not need to be the same flavour.
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
A baryon is a hadron made of three quarks.
The quarks may be of the same or different flavours. For example, the proton consists of \(uud\) quarks and the neutron consists of \(udd\) quarks.
Particles made of two quarks are mesons, not baryons.
Therefore, the correct answer is (B).
Question 38
Topic: 11.4 Radioactive decay.png)
A stationary nucleus has nucleon number \(A\).
The nucleus decays by emitting a proton with speed \(v\) to form a new nucleus with speed \(u\). The new nucleus and the proton move away from one another in opposite directions.
Which equation gives \(v\) in terms of \(A\) and \(u\)?
(B) \(v=(A-1)u\)
(C) \(v=Au\)
(D) \(v=(A+1)u\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{B}} \)
Initially, the nucleus is stationary, so the total momentum is zero.
Applying conservation of momentum,
\(m_pv=(A-1)m_pu\).
Cancelling the proton mass \(m_p\) gives
\(v=(A-1)u\).
Therefore, the correct answer is (B).
Question 39
Topic: 11.3 Quarks and leptons
What is the change to the quark composition of a nucleus that takes place during \(\beta^+\) decay?
(B) down to up
(C) up to antidown
(D) up to down
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
In \(\beta^+\) decay, a proton changes into a neutron by emitting a positron and an electron neutrino.
At the quark level, one up quark changes into a down quark:
\(u\rightarrow d+e^++\nu_e\).
Therefore, the correct answer is (D).
Question 40
Topic: 11.3 Quarks and leptons
What is the charge, in terms of the elementary charge \(e\), on a charm quark?
(B) \(-\dfrac{1}{3}e\)
(C) \(+\dfrac{1}{3}e\)
(D) \(+\dfrac{2}{3}e\)
▶️ Answer/Explanation
Correct Answer: \( \boxed{\mathrm{D}} \)
There are six quark flavours. The up, charm and top quarks each have charge
\(+\dfrac{2}{3}e\).
The down, strange and bottom quarks each have charge
\(-\dfrac{1}{3}e\).
Therefore, the correct answer is (D).