May/June 2023

Which unit is not one of the SI base units?

SI units

A body of mass $m$, travelling with speed $u$ on a smooth horizontal surface, undergoes a head-on collision with a body of mass $4m$ that is initially at rest. Following the collision, the mass-$m$ body moves back along the line of approach with $\frac{1}{4}$ of the kinetic energy it had before the impact. What is the speed of the mass-$4m$ body after the collision?

Linear momentum and its conservation

A car driver exerts two parallel forces on a steering wheel, as illustrated. Each force has a magnitude of $15\,\text{N}$ and acts in the direction shown. The steering wheel has a diameter of $0.40\,\text{m}$. What is the torque exerted on the steering wheel?

Turning effects of forces

A farmer is attempting to raise the corner of a large water tank. She uses a metal rod as a lever. The farmer’s vertical force is constant and is always exerted at the end of the rod. Which change must make the upward force on the water tank larger?

Turning effects of forces

An equilibrium diagram shows a ball of weight $W$ suspended from a string. The string makes an angle $\theta$ with the vertical. The tension in the string is $T$. A metal rod exerts a horizontal force $P$ on the ball, keeping it away from the wall. Which relation between the magnitudes of $T$, $P$ and $W$ is correct?

Equilibrium of forces

Which equation for pressure is correct?

Density and pressure

A ball with a mass of $0.50\,\text{kg}$ and a volume of $1.3 \times 10^{-3}\,\text{m}^3$ is floating in equilibrium on still water. The two forces acting on the ball are its weight and the upthrust due to the water. The density of the water is $1.0 \times 10^3\,\text{kg m}^{-3}$. Calculate the percentage of the ball's volume that is above the water surface.

Density and pressure

A man is riding in a buggy that is being pulled by a wire connected to a kite. The wire makes an angle of $40^\circ$ to the horizontal and maintains a steady tension of $200\,\text{N}$. The man and buggy move $20\,\text{m}$ in a straight horizontal line. The wire and the buggy’s route lie in the same vertical plane. What is the work done by the tension force on the man and buggy?

Energy conservation

A ball is launched straight upwards from the Earth’s surface. Which statement describes the ball’s energy while it moves upward through the air?

Gravitational potential energy and kinetic energy

A lamp hangs in equilibrium from a fixed support, held by three long identical wires. The lamp’s weight makes each wire extend by $0.40\,\text{cm}$. The height $h$ of the lamp above the floor is then measured. The centre wire suddenly snaps, and the lamp drops a short distance while the extensions of the other two wires increase. The wires obey Hooke’s law. When the lamp is again in equilibrium, the height $h$ of the lamp above the floor is measured once more. What is the difference between the two values of $h$?

Stress and strain

A force-extension graph for a spring is displayed. Which quantity corresponds to the work done when the spring is extended?

Elastic and plastic behaviour

What is the most suitable estimate for the number of atoms in a metal piece with volume $50\ \text{cm}^3$?

Atoms, nuclei and radiation

In an experiment, a student uses a microphone together with a cathode-ray oscilloscope (CRO) to investigate a sound wave. The diagram shows the trace displayed on the CRO screen. The student expects a sinusoidal waveform to appear on the screen. Which changes should the student make to the time-base and the $y$-gain of the CRO so that the screen displays a continuous trace for one complete cycle of the waveform?

Progressive waves

The graph illustrates how the displacement of a particle in a progressive wave changes with time. Two readings, $x$ and $y$, are marked on the graph. What do $x$ and $y$ stand for?

Progressive waves

The car moves at constant speed in a straight line PQ. A loudspeaker fixed to the car emits sound with constant frequency $f$. A stationary observer is located at point O. What sound does the observer hear while the car travels from P to Q?

Doppler effect for sound waves

Several sources of electromagnetic waves in free space are shown below. 1. a radio wave transmitter 2. a source of X-rays 3. a $30\,\text{mm}$ wavelength radar transmitter 4. a light-emitting diode that emits red light Which sequence shows the sources arranged from the smallest to the largest wavelength, reading from left to right, of the waves produced by the sources?

Electromagnetic spectrum

A beam of light that is vertically polarised is directed normally at a polarising filter. The filter’s transmission axis makes an angle of $40^\circ$ with the horizontal. What is the ratio $\dfrac{\text{amplitude of transmitted beam}}{\text{amplitude of incident beam}}$?

Polarisation

Two progressive waves arrive together at a point. What condition has to be satisfied for superposition of the waves to occur?

Progressive waves

A string is taut between a vibration generator and a fixed point. When the vibration generator is oscillating with frequency $f$, a stationary wave is formed on the stretched string with five nodes, as shown. A node is present at the end of the string attached to the vibration generator. The frequency of vibration of the vibration generator is then increased slowly. What is the next frequency that produces a stationary wave on the string?

Stationary waves

A ripple tank and a barrier containing one narrow opening are set up to show the diffraction of water surface ripples. At first, the wavelength of the ripples is five times smaller than the width of the gap in the barrier. Which change would make the diffraction more pronounced?

Diffraction

A laser emits light with wavelength $650\,\text{nm}$. This beam is incident normally on two slits separated by $0.12\,\text{mm}$. A screen is set up parallel to the slits. The bright interference fringes on the screen are spaced $7.5\,\text{cm}$ apart. Determine the distance from the screen to the two slits.

Interference

A beam of laser light is incident normally on a diffraction grating. The diagram shows only the second-order maxima that are formed. The grating has a line spacing of $1.0 \times 10^{-6}\,\text{m}$. The angle between the two second-order maxima is $110^{\circ}$. Determine the wavelength of the light.

The diffraction grating

The actual diameter of a copper pipe is $42.03\ \text{mm}$. A builder measures the pipe’s diameter five times using digital calipers. The readings are given below: $48.01\ \text{mm}$ $47.99\ \text{mm}$ $48.01\ \text{mm}$ $48.00\ \text{mm}$ $47.99\ \text{mm}$ Which statement best describes the builder’s measurements?

Errors and uncertainties

A metal wire carries an electric current of $4.0\,\text{mA}$. How many electrons pass a given point in the wire during a time of $10\,\text{hours}$?

Electric current

What does the term potential difference across an electrical component mean?

Potential difference and power

Which graph represents the $I$-$V$ characteristic for a filament lamp?

Resistance and resistivity

The wire is made of metal and initially measures $2.50\,\text{m}$ in length, with a cross-sectional area of $4.50 \times 10^{-6}\,\text{m}^2$. Its resistivity is $3.50 \times 10^{-7}\,\Omega\,\text{m}$. The wire is then pulled so that its length becomes $2.65\,\text{m}$. It stays cylindrical, and the volume of the wire does not change. Calculate the change in the resistance of the wire.

Resistance and resistivity

Which circuit symbol is used for a microphone?

Practical circuits

A battery that has internal resistance is joined to a fixed resistor, an ammeter and a voltmeter, as illustrated. That battery is then swapped for another battery with the same electromotive force (e.m.f.) but a larger internal resistance. What change occurs in the ammeter reading and the voltmeter reading?

Practical circuits

There are four potential divider circuits, and each one is formed from a battery with electromotive force (e.m.f.) $9\,\text{V}$ and negligible internal resistance, linked to a set of resistors. In every circuit, the resistors have resistance values of $X$ or $2X$. Which circuit gives the greatest output voltage $V$?

Potential dividers

A voltmeter is joined to the circuit with the polarity indicated. The sliding contact is shifted to end P of the potentiometer and then moved to end Q. What are the two voltmeter readings?

Potential dividers

The proton is assigned mass $m_p$ and charge $+e$. What are the mass and charge for an antiproton?

Fundamental particles

A uranium nucleus contains 92 protons and 143 neutrons. It emits a total of 3 $\alpha$-particles and 4 $\beta^-$ particles, producing nucleus X. How may nucleus X be represented?

Atoms, nuclei and radiation

At point P, two forces, each of $10\ \text{N}$, act as shown. The angle between their directions is $120^{\circ}$. What is the magnitude of the resultant force?

Scalars and vectors

Which of the following statements about a proton is correct?

Atoms, nuclei and radiation

One object travels straight from P to R. Another object goes from P to Q to R and takes less time. Which statement about the two objects is correct for the trip from P to R?

Scalars and vectors

A ball is launched with an initial velocity of $12\ \text{m s}^{-1}$ at an angle of $50^{\circ}$ above horizontal ground. Assume air resistance is negligible. What maximum height above the ground does the ball reach?

Equations of motion

A camera drone with mass $1.20\,\text{kg}$ remains stationary in the air at a particular point above the ground. The drone is fitted with four propellers. During a period of $1.00\,\text{s}$, each propeller drives $0.400\,\text{kg}$ of air straight downwards. Take the air above the propellers to be at rest. What is the speed of the air as it leaves each propeller?

Momentum and Newton's laws of motion

A box is at rest on the Earth, as shown. Newton’s third law explains that forces of the same kind occur in pairs. One force in the pair is the box’s weight $W$. Which arrow shows the other force in this pair?

Momentum and Newton's laws of motion

A small ball is resting at the surface of a liquid oil in a container. The ball is let go from rest and moves downward through the oil. The ball has velocity $v$. A viscous (drag) force $F$ acts on the ball. Which graph could represent how $F$ varies with $v$?

Non-uniform motion

A stone sinks in water. What could be a possible value of the stone's density?

Density and pressure

Balls X and Y move towards one another along the same straight line and then collide. The collision is perfectly elastic. Their initial speeds are $u_x$ and $u_y$ respectively. After the collision, they separate with speeds $v_x$ and $v_y$ respectively. Their directions are shown. Which equation is right?

Linear momentum and its conservation

The rod is pivoted at point O, and a force $F$ is applied to it at point W, as shown. What moment does the force $F$ produce about O?

Turning effects of forces

A uniform rod XY, with weight $10.0\,\text{N}$, is hinged freely to a wall at X. As shown, it is kept horizontal by a force $F$ applied at Y at an angle of $30^{\circ}$ to the horizontal. What is the value of $F$?

Turning effects of forces

Cubes X and Y are solid and are made from material of the same density. The mass of cube X is twice that of cube Y. The side length of cube X is $x$. The side length of cube Y is $y$. What is the ratio $\frac{x}{y}$?

Density and pressure

As shown, a U-shaped glass tube holds a liquid with density $2000\,\text{kg m}^{-3}$. What is the pressure difference due to the liquid between levels P and Q?

Density and pressure

A steam turbine is employed to turn a generator. The input power to the turbine is $P_I$ and the output power is $P_O$. The power loss in the turbine is $P_L$, as illustrated. What is the efficiency of the turbine?

Energy conservation

A changing force is applied so that the train is supplied with constant power. Which graph best represents how the force $F$ varies with the train’s velocity $v$?

Energy conservation

A block starts from rest and moves a distance $x$ along a straight slope. The slope makes an angle $\theta$ with the horizontal. The slope is frictionless and air resistance is negligible. The acceleration of free fall is $g$. Which expression gives the block's final speed?

Equations of motion

What does the term spring constant of a spring mean?

Elastic and plastic behaviour

A child is holding a slim metal wire that is fastened to a kite. The graph illustrates how the wire’s extension changes as its tension changes. A gust of wind raises the tension from $100\,\text{N}$ to $150\,\text{N}$. What is the increase in the elastic potential energy of the wire caused by the gust of wind?

Elastic and plastic behaviour

Gm, Tm, $\mu$m and pm are each units used for length. Which of these units is the largest, and which is the smallest?

SI units

A microphone picks up a sound wave. The microphone is linked to a cathode-ray oscilloscope (CRO). The pattern of the trace shown on the CRO screen is shown. Which property of the sound wave can be found by using only a horizontal measurement on the screen and the value of a CRO control setting?

Progressive waves

A longitudinal wave is moving from left to right. The graph illustrates how the displacement of the particles changes with distance along the wave at a particular instant in time. Displacements to the right are taken as positive, whereas displacements to the left are taken as negative. Which labelled point indicates a compression?

Transverse and longitudinal waves

A source X produces a sound wave with a steady frequency $f$. This wave is then detected by a stationary detector Y. The frequency measured by Y is smaller than $f$. What could explain this?

Doppler effect for sound waves

A beam of visible light travels in a vacuum. What might its frequency be?

Electromagnetic spectrum

A beam of light that is vertically polarised and has intensity $I_0$ is incident normally on a polarising filter. The filter’s transmission axis makes an angle of $45^{\circ}$ to the vertical. The light that passes through this filter then falls normally on a second filter. The transmission axis of the second filter is horizontal. What is the intensity of the beam of light after it has passed through the second filter?

Polarisation

A stationary wave is produced when two progressive waves move in opposite directions along the same path. Which statement about these two progressive waves is incorrect?

Stationary waves

A loudspeaker set above a tube makes the air inside the tube resonate. A stationary wave is produced with two nodes and two antinodes, as shown. The height of the tube is $60\ \text{cm}$. The speed of sound in air is $340\ \text{m s}^{-1}$. What frequency does the sound have?

Stationary waves

A continuous progressive water wave in a ripple tank travels through an opening in a barrier and undergoes diffraction. The gap width is larger than the wavelength of the wave. Which alteration makes the wave spread out through a greater angle after it passes through the gap?

Diffraction

The diagram is a plan view of a double-slit interference demonstration. $L$ represents a monochromatic light source with a vertical filament. $B$ represents a barrier containing two narrow vertical slits, and $S$ represents a screen on which interference fringes appear. The intensity at the point on the screen at the centre of the fringe pattern is $I$. If one slit is covered, what intensity is found at that same point on the screen?

Interference

A green light beam with wavelength $550\ \text{nm}$ falls normally on a diffraction grating and forms a diffraction pattern on a screen that is $3.5\ \text{m}$ away from the diffraction grating. The third-order maximum on the screen is $0.75\ \text{m}$ from the zeroth-order (central) maximum. Calculate the spacing between two neighbouring slits in the diffraction grating.

The diffraction grating

The following two measurements are given for a solid sphere. mass $= (32.5 \pm 0.1)\,\text{g}$ diameter $= (1.87 \pm 0.04)\,\text{cm}$ These measurements are then used to work out the sphere’s density. What is the percentage uncertainty in the density?

Errors and uncertainties

Which type of charge can be transported by a charge carrier?

Electric current

A resistor with resistance $R$ is joined across a cell of electromotive force (e.m.f.) $E$ and negligible internal resistance. Which one alteration to the circuit would produce the greatest rise in the power dissipated in the resistor?

Potential difference and power

A cable contains one thick copper wire strand and eight thin copper wire strands. These nine strands are all joined in parallel with one another. The cable’s cross-section is shown. Each thin strand has cross-sectional area $A$ and length $L$. The thick strand has cross-sectional area $4A$ and length $L$. The resistance of the complete cable is $R$. Which expression gives the resistivity of copper?

Resistance and resistivity

A car is fitted with sensors to detect the light intensity and temperature of its surroundings. The sensors use a light-dependent resistor (LDR) and a thermistor. The car travels from a warm, dark environment into a cold, bright environment. What changes occur in the resistances of the LDR and thermistor?

Resistance and resistivity

A student constructs the circuit diagrammed below. Which row gives the condition of the two lamps?

Practical circuits

Kirchhoff's first law follows from the conservation of which quantity?

Kirchhoff's laws

Each of the three matching cells has electromotive force (e.m.f.) $E$ and negligible internal resistance. The cells are arranged with three matching resistors, each of resistance $R$, as illustrated. What potential difference is across one resistor?

Kirchhoff's laws

In the potentiometer circuit diagram, the ammeter shows zero. The light-dependent resistor (LDR) is then covered, and the ammeter shows a non-zero reading. Which change could make the ammeter reading zero again?

Potential dividers

What does the term isotopes mean?

Atoms, nuclei and radiation

A neutron $^1_0\text{n}$ strikes a $^{{235}}_{{92}}\text{U}$ nucleus. The neutron is taken in by the nucleus, after which it splits into nuclei of $^{{141}}_{{56}}\text{Ba}$ and $^{{92}}_{{36}}\text{Kr}$. What is the number of free neutrons released when the $^{{235}}_{{92}}\text{U}$ nucleus splits?

Atoms, nuclei and radiation

An aircraft moves in a straight line along a level course. Two horizontal forces acting on the aircraft are the thrust force from the engines and the force produced by the wind. The vector diagram for these forces is shown. Which vector shows the resultant horizontal force on the aircraft caused by these two forces?

Scalars and vectors

A $\pi^+$ meson carries a charge of $+e$, where $e$ is the elementary charge. It is made up of an up quark and one additional quark. What might the other quark in the $\pi^+$ meson be?

Fundamental particles

A ball moves from point X to point Y along a semicircular track with radius $1.0\,\text{m}$, as shown. What is the displacement of the ball from X to Y?

Scalars and vectors

One rock is projected vertically upwards from Earth’s surface, while an identical rock is projected vertically upwards from Mars’ surface. In each case, the rock is given an initial velocity of $12\,\text{m s}^{-1}$. Each rock then rises to its greatest height above the surface and later falls back to the surface. The velocity-time graph for each rock is shown. For both rocks, air resistance is negligible. What is the difference between the maximum heights reached by the two rocks?

Equations of motion

Which statement gives the definition of the mass of an object?

Physical quantities

A submarine with a total mass of $3200\,\text{kg}$ is stationary beneath the water. Its total mass is then reduced by $200\,\text{kg}$, as water is pumped out horizontally from the submarine in a negligible time. The upthrust on the submarine remains the same. Because the total weight of the submarine changes, it accelerates vertically upwards. What is the submarine's initial upwards acceleration?

Momentum and Newton's laws of motion

A box in air moves down a rough slope from point P to point Q with its speed getting greater. The slope surface applies a frictional force of constant magnitude to the box. During the journey from P to Q, the magnitudes of its acceleration and the total resistive force on it change. Which row shows these changes?

Non-uniform motion

What information must a record of a physical quantity contain?

Physical quantities

A perfectly elastic collision takes place between two objects X and Y. The mass of X is $m$ and the mass of Y is $4m$. Before the collision, object X moves with speed $v$, and after the collision it moves in the opposite direction with speed $\frac{3v}{5}$. Object Y is at rest before the collision. Determine the kinetic energy of Y after the collision?

Linear momentum and its conservation

Which of the following is not needed for two forces to form a couple?

Turning effects of forces

A metre rule of uniform density is supported on a pivot at the $34.0\,\text{cm}$ mark, as shown. The rule is in equilibrium when a mass of $64\,\text{g}$ is suspended from the $4.0\,\text{cm}$ mark. What is the mass of the metre rule?

Turning effects of forces

A quantity of $1.5\,\text{m}^3$ of water is combined with $0.50\,\text{m}^3$ of alcohol. The density of water is $1000\,\text{kg m}^{-3}$, while the density of alcohol is $800\,\text{kg m}^{-3}$. The mixture has a volume of $2.0\,\text{m}^3$. Determine the density of the mixture.

Density and pressure

An object is descending through a viscous liquid at a steady speed. $F_u$ represents the upthrust acting on the object because of the liquid. $W_L$ represents the weight of the liquid displaced by the object. $W_o$ represents the weight of the object. Which equation must be true?

Density and pressure

At an airport, luggage is transported by a mechanical arrangement. This arrangement consists of a horizontal conveyor belt, a sloping conveyor belt, a lift and a frictionless slide. A suitcase is carried around the airport by this arrangement. The resistive forces that oppose the motion of the suitcase are negligible. For which movement of the suitcase is the net work done on the suitcase greatest?

Gravitational potential energy and kinetic energy

A car is travelling on a horizontal road at a constant velocity $v$ while a resistive force $F$ acts on it. The engine of the car has an efficiency of $25\%$. What is the input power to the engine?

Energy conservation

A projectile of mass $0.40\,\text{kg}$ is launched into the air and travels along a curved trajectory above level ground. It remains in motion for $1.5\,\text{s}$ before reaching the ground again. The landing point is $18\,\text{m}$ horizontally from where it started. Air resistance can be ignored. Calculate the kinetic energy of the object when it is at its highest point.

Equations of motion

A metal wire is $5.2\,\text{m}$ long and has a diameter of $1.0\,\text{mm}$. Its Young modulus is $360\,\text{GPa}$. One end of the wire is held fixed, and a force is exerted on the other end. This force produces an extension of $7.2\,\text{mm}$ in the wire. Assume Hooke’s law applies. What is the force applied to the wire?

Stress and strain

The graph indicates how the spring’s length changes with the force exerted on it. The spring has unstretched length $L_0$. If a force $F$ is applied, the spring then has length $L_1$. What is the work done in extending the spring to length $L_1$?

Elastic and plastic behaviour

How is the ohm written in SI base units?

SI units

A progressive wave has a frequency of $1.5\,\text{kHz}$ and moves through a medium with a speed of $340\,\text{m s}^{-1}$. What is the smallest distance between two points on the wave that are separated by a phase difference of $70^{\circ}$?

Progressive waves

Graph 1 plots how displacement varies over time at a fixed point on a progressive wave. Graph 2 shows the same wave and plots how displacement changes with distance at a particular instant. What is the wave speed?

Progressive waves

A vehicle travels at constant velocity along a road straight towards an observer. As it goes past the observer, the frequency detected from the vehicle’s sound alters. Which phenomenon accounts for this change in frequency?

Doppler effect for sound waves

A wave in the electromagnetic spectrum has a wavelength of $2.1\,\text{cm}$ in a vacuum. In which region of the electromagnetic spectrum does this wave lie?

Electromagnetic spectrum

A source of plane polarised light is viewed through two polarising filters. The filters are arranged so that the source is seen at maximum brightness. One filter is then turned clockwise and the other is turned anticlockwise by the same amount. What is the appearance of the source when both filters have been rotated $90^{\circ}$ and $180^{\circ}$ from their starting positions?

Polarisation

The diagram depicts a string held taut between the fixed points X and Y. A stationary wave is present on the string. The solid line indicates the string when its displacement is greatest at time $t_0$. The dashed line indicates the alternative position of greatest displacement. The straight dashed line in the middle represents the mean position of the string. Point S on the string is vertically above point P. Point T on the string is vertically below point Q. Which statement is correct?

Stationary waves

The graph shows how the intensity $I$ varies with distance $x$ in a stationary sound wave in air. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the frequency of the sound wave?

Stationary waves

An experiment is arranged to show the diffraction of water waves in a ripple tank. The waves travel through a gap of width $w$, and diffraction of the waves is seen. The wavelength of the waves is now doubled. What new gap width is required to produce the same degree of diffraction as before?

Diffraction

Two coherent electromagnetic waves are moving through a vacuum. The two waves overlap at one point. At this point, the two waves have unequal intensities. Which statement about the waves is not correct?

Interference

A parallel beam of light with wavelength $600\,\text{nm}$ is incident at right angles onto a diffraction grating. The separation between neighbouring slits in the grating is $2.0 \times 10^{-6}\,\text{m}$. A screen is set up parallel to the grating, $1.50\,\text{m}$ away from it. Third-order diffraction maxima appear at the two edges of the screen, as shown. What is the separation between the two ends of the screen?

The diffraction grating

The actual width of a desk is $50.0\,\text{cm}$. Two learners, X and Y, are measuring the desk's width. Learner X uses a tape measure and obtains a width of $(49.5 \pm 0.5)\,\text{cm}$. Learner Y uses a metre rule and obtains a width of $(51.4 \pm 0.1)\,\text{cm}$. Which statement about learner X's measurement is correct?

Errors and uncertainties

A metal wire is joined between the terminals of a cell, causing a current to flow through the wire. Which statement is correct?

Electric current

A battery with electromotive force (e.m.f.) $12\,\text{V}$ and negligible internal resistance is connected in parallel to two resistors whose resistances are $R$ and $2R$. The combined power dissipated in the two resistors is $36\,\text{W}$. What is $R$?

Potential difference and power

A metal wire is $3.0\,\text{m}$ long and is made from a material with resistivity $4.9 \times 10^{-7}\,\Omega\,\text{m}$. A potential difference (p.d.) of $12\,\text{V}$ is placed across the wire, causing a current of $1.4\,\text{A}$ to flow. Calculate the cross-sectional area of the wire.

Resistance and resistivity

A cell with negligible internal resistance is connected in series to a thermistor, a fixed resistor and an ammeter. The thermistor is put into a beaker containing water, and the water temperature is raised slowly. A graph of current $I$ plotted against the thermistor temperature $T$ is drawn. Which graph might represent how $I$ changes with $T$?

Resistance and resistivity

A battery with internal resistance is connected to two resistors in parallel and a switch $S$, as illustrated. At first, switch $S$ is open. What changes in the voltmeter and ammeter readings when switch $S$ is closed?

Practical circuits

Kirchhoff’s first law says that, at a junction in a circuit, the total current flowing in is equal to the total current flowing out. This law is founded on the conservation of a physical quantity. What is this physical quantity?

Kirchhoff's laws

When the two resistors are joined in series, their total resistance is $34\,\Omega$. When the same two resistors are joined in parallel, their total resistance is $7.4\,\Omega$. What is the resistance of one resistor?

Resistance and resistivity

A potentiometer circuit is employed to determine the electromotive force (e.m.f.) of a cell $X$. The e.m.f. of cell $X$ is approximately $0.50\,\text{V}$. The driver cell has an e.m.f. of $2.0\,\text{V}$ and negligible internal resistance. The sliding contact is then shifted along the uniform resistance wire from end $Q$ to end $R$ until it reaches a position $P$ where the galvanometer shows zero. What expression gives the approximate length $QP$?

Potential dividers

The table gives information about four nuclei, P, Q, R and S. Which pair of nuclei are isotopes of the same element?

Atoms, nuclei and radiation

Which statement concerning $\beta^{-}$ decay is correct?

Atoms, nuclei and radiation

The scale drawing shows vectors $X$ and $Y$. If $X = Y - Z$, which diagram shows the vector $Z$?

Scalars and vectors

What quark composition makes up a hydrogen-3 nucleus, $^3_1\text{H}$?

Fundamental particles

Which equation for uniformly accelerated motion along a straight line can be found using only the definition of acceleration?

Equations of motion

An object starts from rest and travels with constant velocity in the horizontal direction and constant acceleration in the vertical direction. Which graph correctly shows how the object’s displacement from its starting position changes with time?

Equations of motion

A paint-spraying device is made from a box whose faces are arranged horizontally and vertically. Small openings are present in one of the vertical faces. Paint is supplied into the box at pressure through a vertical tube, then leaves the openings as narrow jets travelling horizontally. The paint leaves at a speed of $2.5\,\text{m s}^{-1}$ through $400$ holes, each with area $0.4\,\text{mm}^2$. The density of the paint is $900\,\text{kg m}^{-3}$. Calculate the horizontal force needed to keep the device at rest while the paint is being sprayed.

Linear momentum and its conservation

Each diagram shows two forces with the same magnitude. Which diagram shows a pair of forces that Newton’s third law of motion describes?

Momentum and Newton's laws of motion

Two balls with the same shape and size but different masses are falling through the same liquid. For each ball, the combined drag force and upthrust on it is equal to its weight. Which statement about the two balls is correct?

Non-uniform motion