May/June 2025

Which quantity has vector properties?

Scalars and vectors

A firework moves straight upwards through the air. Gases are driven vertically downwards from the firework. The diagram shows several forces acting on the firework and on the gases. Which forces form a Newton’s third law pair?

Momentum and Newton's laws of motion

Blocks K and L move towards one another on a horizontal frictionless surface. The diagram indicates the momentum of the two blocks immediately before they collide. While the collision takes place, the blocks remain in contact for $0.084\,\text{ s}$. Once the collision is over, the blocks move apart and block L travels back along its initial path with momentum $0.12\,\text{kg m s}^{-1}$. Determine the magnitude of the average force on block L due to block K during the collision.

Momentum and Newton's laws of motion

Leonardo da Vinci suggested a flying machine designed to act like a screw and raise the pilot into the air. The pilot turns the ‘screw’. The combined mass of the machine and the pilot is $120\,\text{kg}$. Which useful output power is needed for the pilot to travel straight upwards at a steady speed of $2.5\,\text{m s}^{-1}$?

Gravitational potential energy and kinetic energy

Which row identifies a pair of forces that makes a couple?

Turning effects of forces

A uniform cylinder with weight $25.0\,\text{N}$ is hanging from a newton meter. The cylinder is completely immersed in water, as shown. The newton meter shows a reading of $10.0\,\text{N}$. The water is then changed to a liquid whose density is $10\%$ greater than the density of water. The cylinder is still completely submerged. What reading will the newton meter now show?

Density and pressure

A student supports a $30\,\text{cm}$ ruler on a fulcrum positioned at the $15\,\text{cm}$ mark. She then puts a $50\,\text{g}$ mass at the $23\,\text{cm}$ mark and a $20\,\text{g}$ mass at the $11\,\text{cm}$ mark, as illustrated. Which mass should she put on the $7\,\text{cm}$ mark to make the ruler balance again?

Turning effects of forces

A submarine is located at a depth of $130\,\text{m}$ beneath the sea surface. The pressure acting on the submarine because of the sea water is $p$. The submarine then moves down to a depth of $260\,\text{m}$ beneath the surface. Assume the density of sea water remains constant. What is the difference between the pressures on the submarine due to the sea water at these two depths?

Density and pressure

An object is dropping through a uniform gravitational field. Which two quantities are enough to determine the change in gravitational potential energy?

Gravitational potential energy and kinetic energy

The points X, Y and Z lie on a rough, horizontal surface. A box P is pushed over the surface from X to Y and then from Y to Z. The distance from X to Y is $3.0\,\text{m}$. The work done against the frictional force in moving the box from X to Y is $150\,\text{J}$. The work done against the frictional force in moving the box from Y to Z is $200\,\text{J}$. An identical box Q is pushed in a straight line from X to Z. The size of the frictional force between the boxes and the surface remains constant. How much more work is done against the frictional force in moving P than Q?

Energy conservation

A car with mass $m$ has its momentum rise from $p_1$ to $p_2$. What is the change in the car’s kinetic energy?

Linear momentum and its conservation

Four students, A, B, C and D, have finished an experiment aimed at finding the acceleration of free fall, $g$. Each student carried out the experiment three times. The measured values of $g$ are listed in the table. Which set of results shows high precision but low accuracy?

Errors and uncertainties

A parachutist is descending at constant (terminal) velocity. Which statement is incorrect?

Equilibrium of forces

A student carries out an investigation on a spring. The graph shows how the length of the spring changes with the force acting on the spring. What is the spring constant of the spring?

Elastic and plastic behaviour

The graph illustrates how the extension of a wire changes as the force varies. The force is increased little by little to a peak at Q and then reduced gradually back to zero at R. Which of the following statements is correct?

Elastic and plastic behaviour

A metal wire of uniform cross-section, with length $L$ and diameter $d$, has spring constant $k$. What is the Young modulus of the metal?

Stress and strain

An aircraft emits a sound with frequency of $30.0\,\text{Hz}$. The speed of sound in air equals $330\,\text{m s}^{-1}$. The aircraft is positioned directly in front of a stationary observer and moves in a straight line either towards the observer or away from the observer. The observer detects the aircraft’s sound at a frequency of $20.0\,\text{Hz}$. What is the aircraft’s speed and direction?

Doppler effect for sound waves

Which statement correctly describes longitudinal and transverse wave motion in a progressive wave?

Transverse and longitudinal waves

The diagram illustrates a progressive transverse wave on a stretched string at a particular moment. A point on the string is marked X. Which point on the string is $270^\circ$ out of phase with X?

Progressive waves

Which wavelength of electromagnetic radiation in free space could correspond to green light?

Electromagnetic spectrum

Which group consists solely of waves that are able to be polarised?

Polarisation

The amplitude of one wave is $2A$. A second wave has amplitude $\frac{A}{2}$. Apart from that, the two waves are the same. The waves move in opposite directions and superpose. What is the ratio $\frac{\text{maximum amplitude of combined wave}}{\text{minimum amplitude of combined wave}}$?

Stationary waves

A ball’s diameter is measured to be $(5.26 \pm 0.02)\,\text{cm}$. Calculate the absolute uncertainty in the ball’s volume.

Errors and uncertainties

Light of wavelength $680\,\text{nm}$ falls normally on a diffraction grating with $450$ lines $\text{mm}^{-1}$. What angle of diffraction corresponds to the second-order maximum in the diffraction pattern produced?

The diffraction grating

A hollow tube has one end closed and the other end open. A stationary sound wave with the minimum possible frequency, $820\,\text{Hz}$, is set up in the tube. The speed of sound in air is $330\,\text{m s}^{-1}$. How long is the tube?

Stationary waves

Which equation gives the definition of resistance?

Resistance and resistivity

The graph gives the $I$-$V$ characteristic of an electrical component. What component is this?

Resistance and resistivity

The diagram depicts six identical resistors arranged in a circuit. In which branch of the circuit is the greatest power dissipated?

Potential difference and power

The diagram illustrates a circuit made up of a thermistor, a fixed resistor and a battery. The graph gives the $I$-$V$ characteristics for both components. The battery has an e.m.f. of $12\,\text{V}$ and negligible internal resistance. What current flows through the fixed resistor?

Practical circuits

Two resistors with resistances $R_1$ and $R_2$ are joined in parallel. What is the total resistance between X and Y?

Resistance and resistivity

A cell is arranged in series with an ammeter and a variable resistor. A voltmeter is used to measure the p.d. across the variable resistor. The resistance of the variable resistor is changed, and the p.d. and current are noted. The graph shows how the p.d. across the variable resistor varies with current. What is the internal resistance of the cell?

Practical circuits

Which list includes only fundamental particles?

Fundamental particles

What statement accounts for alpha-particles having discrete energies, while beta-particles show a continuous range of energies?

Atoms, nuclei and radiation

The two vectors, $\vec{X}$ and $\vec{Y}$, are illustrated. In which directions do $\vec{X} + \vec{Y}$ and $\vec{X} - \vec{Y}$ point?

Scalars and vectors

A hadron is made up of antiquarks that are all the same. What could be a possible value, in terms of the elementary charge $e$, for the hadron’s charge?

Fundamental particles

A ball is launched vertically downward with an initial velocity of $20\,\text{m s}^{-1}$. Air resistance may be neglected. What is the displacement from its starting position of the ball after $1.5\,\text{s}$?

Equations of motion

A surveyor’s device sends out a light pulse. The light is reflected by a wall $150\,\text{m}$ away. What is the total time required for the pulse to travel to the wall and return to the device?

Progressive waves

Which equation for uniformly accelerated motion can be obtained using only the gradient of a velocity-time graph?

Equations of motion

At time $t = 0$, an object is launched horizontally from a table. It moves in a uniform gravitational field. Air resistance is negligible. Graphs P, Q, R and S show velocity-time graphs. Which graphs show the horizontal and vertical components of the object’s velocity?

Equations of motion

What quantity is always conserved in elastic collisions?

Linear momentum and its conservation

What must every physical quantity possess?

Physical quantities

Which statement is not used to describe an elastic collision between two objects?

Linear momentum and its conservation

A cyclist travels at a steady speed along a flat road. By Newton’s third law of motion, what force is equal in size and opposite in direction to the backward push exerted by the back wheel on the road?

Momentum and Newton's laws of motion

A stone is dropped from rest and descends a large distance through air. Which graph could represent how the acceleration $a$ of the stone changes with time $t$?

Non-uniform motion

A cart with no load is travelling along a level track at a steady velocity. The resistive forces on the cart are negligible. A heavy rock is dropped straight down into the cart. The cart then keeps moving horizontally with the rock inside it. How do the momentum and kinetic energy of the cart with the rock inside compare with the momentum and kinetic energy of the empty cart?

Linear momentum and its conservation

A wooden block is kept at rest in a container of water by means of a string fixed to both the wooden block and the base of the container. The wooden block has mass $m$ and volume $V$. The water has density $\rho$. The acceleration of free fall is $g$. What is the magnitude of the force exerted on the block by the tension in the string?

Equilibrium of forces

A square shop sign with uniform density has a mass of $2.4\,\text{kg}$ and side length $0.86\,\text{m}$. It is held up by a hinge fixed along its top edge. Because there is friction in the hinge, the sign hangs in equilibrium at an angle of $15^{\circ}$ to the vertical, as shown. Calculate the moment about the hinge due to the sign’s weight.

Turning effects of forces

A block is immersed vertically in a liquid. The four diagrams show the block as viewed from the side. Which diagram shows, to scale, the forces produced by the liquid on equal areas of the block?

Density and pressure

The diagram depicts a couple. How is the torque of the couple found?

Turning effects of forces

A ball with a mass of $1.2\,\text{kg}$ is moving horizontally at $3.0\,\text{m s}^{-1}$. It strikes a cushion and then stops after covering a horizontal distance of $0.020\,\text{m}$. What work is done by the cushion on the ball in order to bring the ball to rest?

Energy conservation

A block with mass $4.9\,\text{kg}$ is moved at steady speed from point P at the foot of an inclined plane to point Q at the summit. A force of $64\,\text{N}$, applied parallel to the slope, pushes the block. The plane is set at an angle of $20^\circ$ to the horizontal, and the block rises through a vertical distance of $5.8\,\text{m}$. What is the work done against the frictional force acting on the block between P and Q?

Gravitational potential energy and kinetic energy

How is $0.25\,\text{N mm}^{-2}$ written in $\text{N m}^{-2}$?

Density and pressure

Which formula shows the efficiency of a system?

Energy conservation

A student has one copper wire and one steel wire that are the same length and have the same cross-sectional area. The student applies identical loads to both wires. The two wires extend by different amounts. The student works out the stress, strain and Young modulus for each wire. Which row shows with a tick (✓) the calculated quantities that are the same for both wires?

Stress and strain

Springs X and Y undergo elastic extension. The graphs illustrate how the applied force $F$ varies with extension $x$ for each spring. Which statement is correct?

Elastic and plastic behaviour

What phrase is used to describe the strain at the elastic limit on a stress-strain graph?

Stress and strain

A teacher takes the turntable out of a microwave oven and puts a bar of chocolate inside the oven. She then turns the oven on for a brief period. A stationary wave is produced inside the oven. After the chocolate is taken out, the teacher notices two small melted regions of chocolate $6.0\,\text{cm}$ apart, with chocolate that has not melted between them. Each melted region is positioned at an antinode. Assume that the microwaves travel at $3.0 \times 10^8\,\text{m s}^{-1}$. What is the frequency of the microwaves emitted by the oven?

Stationary waves

A sound wave moves from left to right. At one moment, the graph shows how the displacement of particles in the sound wave to the right varies with distance. Which letter shows the centre of a compression?

Transverse and longitudinal waves

A buzzer that produces sound at a frequency of $846\,\text{Hz}$ is fixed to a string and spun in a horizontal circle. Its linear speed is $25.0\,\text{m s}^{-1}$. Take the speed of sound as $340\,\text{m s}^{-1}$. What is the largest frequency detected by the observer?

Doppler effect for sound waves

Light with intensity $I_0$ that is vertically polarised is incident normally on a polarising filter. The filter’s transmission axis makes an angle $\theta$ with the plane of polarisation of the light. After the light passes through the filter, its intensity becomes $\dfrac{I_0}{3}$. What is $\theta$?

Polarisation

Which statement makes a comparison between the behaviour of transverse waves and longitudinal waves?

Transverse and longitudinal waves

A student uses a diffraction grating to find the wavelength of visible light from a source. The diffraction grating has 300 lines per mm. For each order $n$ of the intensity maxima, the student measures the angle $\theta$. A graph of $n$ against $\sin \theta$ is drawn. The plotted points are fitted with a line of best fit, and this line has gradient $G$. Which expression gives the wavelength, in m, of the visible light in terms of $G$?

The diffraction grating

A student determines the density of a solid steel cube during an experiment. The recorded mass is $975\,\text{g} \pm 10\,\text{g}$ and the recorded side length is $50\,\text{mm} \pm 1\,\text{mm}$. What value is obtained for the density of the steel?

Density and pressure

Two waves overlap. Which of the following is not a required condition for them to form a stationary wave?

Stationary waves

A single-wavelength light beam is incident normally on a double slit. A pattern of interference fringes is seen on a screen. The separation between the double slit and the screen is $0.60\,\text{m}$, and the fringe spacing is $1.8\,\text{mm}$. If the distance between the double slit and the screen is increased by $0.90\,\text{m}$, what will the new fringe spacing be?

Interference

A wire is made from a metal with constant resistivity. A constant current flows in the wire. Which statement about the potential difference across the wire is correct?

Resistance and resistivity

The $I- V$ characteristics of three electrical components are shown. Which of these components obey Ohm’s law?

Resistance and resistivity

A resistor with a resistance of $200\,\Omega$ is connected to a supply with a p.d. of $4.00\,\text{V}$. How many electrons move into the resistor in $4.00\,\text{s}$?

Electric current

The diagram depicts a cell with internal resistance $1.0R$ connected to a variable resistor. When the variable resistor is first set to a resistance of $2.0R$, the current in the cell is $I_1$ and the terminal potential difference (p.d.) across the cell is $V_1$. The variable resistor is then changed to a resistance of $4.0R$. What are the new current in the cell and the new terminal p.d. across the cell?

Practical circuits

The diagram depicts a four-terminal box connected to a battery and two ammeters. The readings on the two ammeters are the same. Which circuit inside the box produces this outcome?

Practical circuits

Each of Kirchhoff’s two laws assumes conservation of a quantity. Which row gives Kirchhoff’s first law and identifies the conserved quantity?

Kirchhoff's laws

Two neutral atoms are isotopes of the same element. Select the correct statement about them.

Atoms, nuclei and radiation

Which particles make up a meson?

Fundamental particles

The period $T$ of a pendulum is defined by $T = 2\pi \left(\frac{L}{g}\right)^n$ where $L$ denotes the length of the pendulum and $g$ denotes the acceleration due to free fall. This equation is homogeneous. What value does $n$ take?

Physical quantities

The nucleus of carbon-11 has 6 protons and 5 neutrons. This carbon-11 nucleus undergoes decay by $\beta^+$ emission. What is the total number of up and down quarks in the daughter nucleus formed after this decay?

Fundamental particles

Radio waves may be used to find the separation between Earth and the planet Jupiter. A pulse of radio waves is sent out from the surface of Earth. The pulse is reflected by the surface of Jupiter and then received back on Earth. The interval between transmission and reception of the pulse is $3960\,\text{s}$. What is the distance between Earth and Jupiter?

Electromagnetic spectrum

The graph indicates how the car’s velocity changes over time. Which statement is correct?

Equations of motion

A solid object with mass $1.0\,\text{kg}$ is moving straight down in a vacuum. At the moment its speed reaches $60\,\text{m s}^{-1}$, an extra constant force of $50\,\text{N}$ begins to act on the object vertically upwards. Find the speed of the object $2.0\,\text{s}$ after this additional force starts acting.

Momentum and Newton's laws of motion

A stone is thrown upwards and moves along a curved trajectory. Air resistance can be ignored. Why is the trajectory shaped like this?

Equations of motion

A rocket engine expels $90\,\text{kg}$ of exhaust gas each second at a speed of $190\,\text{m s}^{-1}$ relative to the rocket. What force acts on the rocket as a result of the ejected gas?

Linear momentum and its conservation

What is meant by a vector quantity?

Scalars and vectors

Four forces, each lying in the same plane, act on an object. What might describe the object's motion?

Momentum and Newton's laws of motion

A nucleus strikes a nucleus that is at rest in a vacuum. The diagrams display the nuclei’s trajectories before the collision and after it. There are no other particles taking part in the collision. Which diagram cannot occur?

Linear momentum and its conservation

A non-uniform bar PQ is 50\,\text{cm} long and has weight 200\,\text{N}. A block of weight 400\,\text{N} is fixed at the centre of the bar. The bar is supported on horizontal ground. An upward vertical force of 360\,\text{N} is then applied at end Q and is just enough to raise end Q clear of the ground. What is the distance from the centre of gravity of the bar to end P?

Turning effects of forces

What does the term density mean?

Density and pressure

A block is in equilibrium on an inclined plane. Which vector triangle corresponds to the three forces on the block?

Equilibrium of forces

A measuring cylinder holds $80\,\text{cm}^3$ of a liquid. At the $60\,\text{cm}^3$ mark, the pressure caused by the liquid is $1200\,\text{Pa}$. What is the pressure caused by the liquid at the bottom of the measuring cylinder?

Density and pressure

Four identical uniform blocks are arranged on a table. Each block has mass $m$ and thickness $h$. The acceleration of free fall is $g$. What amount of work is done on the blocks when they are stacked one on top of another?

Gravitational potential energy and kinetic energy

An electric motor consumes $1.7\,\text{kW}$ of power while running normally. The motor's efficiency is $53\%$. What is the motor’s useful output power?

Potential difference and power

A ball is let go from rest and drops straight down to the ground. The kinetic energy $E_K$ of the ball changes as the height $h$ of the ball above the ground changes. Air resistance is negligible. Which graph shows how $E_K$ varies with $h$?

Gravitational potential energy and kinetic energy

An object moving at a speed of $10\,\text{m s}^{-1}$ has a kinetic energy of $1500\,\text{J}$. Its speed is then raised to $40\,\text{m s}^{-1}$. Calculate the new kinetic energy of the object.

Gravitational potential energy and kinetic energy

What would be a sensible estimate for the current in an electric kettle while it is operating?

Electric current

What units are used for stress, strain and the Young modulus?

Stress and strain

A force-extension graph for a metal wire is shown. What quantity does the area beneath the graph represent?

Elastic and plastic behaviour

A wire with original length $L_0$ is fixed at one end. A tensile force is then exerted on the other end, causing the wire to stretch to a new length $L_1$. What is the strain of the wire?

Stress and strain

A wire with length $L$ is stretched so that its limit of proportionality can be found. The graph illustrates how the extension $x$ changes as the force $F$ applied to the wire changes. On the graph, point $P$ marks the limit of proportionality. The test is then carried out again using a different wire of length $2L$, made from the same material and having the same diameter as the first wire. Which point on the graph indicates the limit of proportionality for the new wire?

Elastic and plastic behaviour

The graph illustrates how the displacement of water particles changes with distance along the wave at one specific instant for a transverse water wave. $P$, $Q$ and $R$ indicate the locations of three water particles in the wave. Which particle has the largest speed at the instant shown?

Progressive waves

Which phenomenon occurs only in transverse waves?

Polarisation

An oscilloscope shows a wave. The oscilloscope is set to: time-base: $300\,\mu\text{s\,div}^{-1}$ y-gain: $40\,\mu\text{V\,div}^{-1}$ What is the frequency of the wave?

Progressive waves

An electromagnetic wave moving through free space cannot be seen by the human eye. What could be a suitable wavelength for the wave?

Electromagnetic spectrum

Two sources, X and Y, produce electromagnetic waves with matching wavelengths. The waves from X and Y are emitted with a phase difference of $180^{\circ}$. A detector is moved along a route parallel to the line XY, where it records a sequence of intensity maxima and minima. The diagram illustrates the positions of the sources and the detector path. An intensity maximum is found at point Z. The distance XZ is $70\ \text{cm}$ and the distance YZ is $110\ \text{cm}$. What could be a possible wavelength of the waves?

Interference

Two waves of the same kind overlap. At what point does the principle of superposition apply?

Interference

Which of the following statements about measurement errors is correct?

Errors and uncertainties

In a ripple tank, the water is at a fixed depth. A water wave with constant frequency moves towards a gap in a barrier in the ripple tank. The gap is reduced in width. Which diagram shows the wave before and after the barrier?

Diffraction

Light of one frequency from two coherent sources produces alternating bright and dark fringes on a screen by interference. Which change would give a greater fringe separation?

Interference

For a metallic conductor with cross-sectional area $A$, the current $I$ is expressed as $I = Anve$ where $e$ denotes the elementary charge and $v$ is the average drift speed of the conduction electrons. What does the symbol $n$ stand for in this equation?

Electric current

Which charge cannot be carried by a charge carrier?

Electric current

A steel wire of length $2.20\ \text{m}$ is joined to a battery, as illustrated. The voltmeter shows $1.50\ \text{V}$, while the ammeter shows $4.90\ \text{A}$. Steel has a resistivity of $6.90 \times 10^{-7}\ \Omega\,\text{m}$. Determine the diameter of the steel wire.

Resistance and resistivity

A cell with e.m.f. $8.0\,\text{V}$ is connected to two resistors of resistance $R$ and two resistors of resistance $3R$, as illustrated. The cell’s internal resistance is negligible. What reading does the voltmeter show?

Practical circuits

A battery has an e.m.f. $E$ and internal resistance $r$. It supplies a current $I$ to a variable resistor, and the p.d. at its terminals is $V$. The variable resistor is adjusted so that $I$ gets larger. Why does $V$ fall?

Practical circuits

A fixed-resistance electrical device of $20\,\Omega$ is joined in series with a variable resistor and a battery with e.m.f. $16\,\text{V}$ and negligible internal resistance. The electrical device dissipates $4.0\,\text{W}$ of power. What resistance does the variable resistor have?

Potential difference and power

A nucleus undergoes decay by releasing a $\beta^+$ particle. Which other particle has to be emitted by the nucleus as well?

Atoms, nuclei and radiation

What is the charge on an antidown quark, and what is the charge on an antistrange quark?

Fundamental particles

A piece of material has cross-sectional area $A$ and length $L$. The temperatures on the two faces of the sample are $T_1$ and $T_2$. Thermal energy $Q$ passes through the sample in time $t$. These quantities obey $\frac{Q}{t} = k \times A \times \frac{(T_1 - T_2)}{L}$, where $k$ is a constant. Determine the SI base units of $k$.

SI units

The nucleus of a radioactive isotope belonging to an element releases an $\alpha$-particle. Next, the daughter nucleus produced then releases a $\beta^-$ particle, and after that the daughter nucleus from this decay releases another $\beta^-$ particle. Which statement describes the final nuclide that is produced?

Atoms, nuclei and radiation

The graph illustrates how velocity changes with time $t$ for an object travelling in a straight line. When $t = 0$, the object's displacement is zero. What is the displacement of the object at $t = 20\,\text{s}$?

Equations of motion

A science museum arranges an experiment to demonstrate the descent of a feather inside a vertical glass vacuum tube. The time taken to fall from rest in the vacuum should be about $0.5\,\text{s}$. Which tube length is needed?

Equations of motion

Two coins are launched from a level table with the same initial speed $u$. Coin X is launched horizontally. Coin Y is launched at an angle of $30^\circ$ above the horizontal. Both coins strike the horizontal ground and do not rebound. Assume that the air resistance acting on each coin is negligible. Which statement about the motion of the coins is correct?

Equations of motion

Two spheres are dropped from rest from the same height above the ground. Each sphere attains terminal velocity. One sphere has a greater density than the other sphere, and the two spheres have the same volume. Which statement is correct when both spheres are moving at terminal velocity?

Non-uniform motion

Which statement gives the definition of force?

Momentum and Newton's laws of motion