Oct/Nov 2017

Which SI unit, when expressed in base units, is incorrect?

SI units

What does the principle of conservation of momentum state?

Linear momentum and its conservation

Two solid spheres make up an isolated system. Sphere X is travelling at a speed of $6\,\text{cm s}^{-1}$ along a straight path directly towards sphere Y, which is stationary, as illustrated. The spheres undergo a perfectly elastic collision. Once the collision is over, sphere X continues in the same direction as before the collision but now with a speed of $2\,\text{cm s}^{-1}$. What is the speed of sphere Y?

Linear momentum and its conservation

A block is immersed vertically in a liquid. The four diagrams, drawn to scale, illustrate the forces that the liquid exerts on the block. Which diagram correctly represents a possible situation when viewed from the side?

Density and pressure

A rigid circular disc with radius $r$ has centre X. Several forces, each with the same magnitude $F$, act at the rim of the disc. Every force lies in the plane of the disc. Which arrangement of forces gives a moment of magnitude $2Fr$ about X?

Turning effects of forces

The diagram represents a motorised vehicle designed to transport one person. The vehicle has two wheels mounted on the same axle. The passenger stands on a platform positioned between the wheels. The weight of the machine is $600\,\text{N}$. Its centre of mass is $200\,\text{mm}$ in front of the axle. The wheel radius is $400\,\text{mm}$. When the vehicle is stationary, a passenger with weight $600\,\text{N}$ stands with his centre of mass $200\,\text{mm}$ behind the axle so that the machine is balanced. The motor is now turned on so that a horizontal force of $90\,\text{N}$ acts at the ground and drives the vehicle forwards. How far, and in what direction, must the passenger shift his centre of mass to keep the machine balanced?

Turning effects of forces

Deriving the pressure equation $\Delta p = \rho g \Delta h$ involves several relationships between quantities. Which relationship is not included in the derivation of this equation?

Density and pressure

Power is passed through a machine as illustrated. What is the efficiency of the machine?

Energy conservation

A piston in a gas supply pump has an area of $400\,\text{cm}^2$. This pump forces the gas against a constant pressure of $3000\,\text{Pa}$. For part of the stroke, the piston travels $25\,\text{cm}$ in one direction. What amount of work is carried out by the piston in this motion?

Density and pressure

A stone is launched straight upwards from the ground with an initial speed of $15\,\text{m s}^{-1}$. Air resistance is negligible. What is the greatest height attained by the stone?

Equations of motion

A turbine in a hydroelectric power station lies $30\,\text{m}$ beneath the surface of a large lake. Water flows through the turbine at a rate of $340\,\text{m}^3$ each minute. The combined efficiency of the turbine and generator system is $90\%$. Calculate the power output of the station. (The density of water is $1000\,\text{kg m}^{-3}$.)

Gravitational potential energy and kinetic energy

As shown, at point $P$ there are two forces, each with magnitude $10\,\text{N}$. The angle between their directions is $120^\circ$. What is the magnitude of the resultant force?

Scalars and vectors

A spring is placed under load with weights. After the weights are taken away, the spring returns to its starting length. The spring is then placed under a larger load with heavier weights. When those weights are removed, the spring remains longer than its starting length. Which types of deformation are demonstrated by this experiment?

Elastic and plastic behaviour

A stress-strain graph for a metal is provided. What is the strain energy per unit volume of a rod made from this metal when the rod’s strain is $0.010$?

Stress and strain

A displacement-time graph for a layer of air in the path of a sound wave is shown. Which wave quantity is increasing?

Progressive waves

A loudspeaker sends a sound wave along a tube that is, at the start, completely filled with water. The tap at the base of the tube is then opened, allowing the water to drain out slowly. At certain lengths of the air column in the tube, the sound that is heard becomes much louder. The first very loud sound is heard when the air column in the tube has length $x$. The next occasion on which a very loud sound is heard is when the air column in the tube has length $y$. What is the wavelength of the sound wave from the loudspeaker?

Stationary waves

Diffraction may be seen when a wave goes past an obstacle. The diffraction effect is most pronounced when the wavelength and the obstacle are of comparable size. For waves moving through air, what pairing of wave and obstacle would show diffraction most clearly?

Diffraction

The Sun emits light with a specific wavelength $\lambda_s$. However, at a given moment, the Earth records a spread of wavelengths extending from values below $\lambda_s$ to values above $\lambda_s$. This happens because of the Doppler effect. What might account for this Doppler effect?

Doppler effect for sound waves

What is the approximate order of magnitude for the frequencies of electromagnetic waves in the visible spectrum?

Electromagnetic spectrum

Two signals move towards one another, as shown. At one moment, the signals are exactly on top of each other. Using the principle of superposition, what shape does the combined signal have at this moment?

Progressive waves

Coherent waves are generated at P and at Q, then move outwards in all directions. The line RS is exactly halfway between P and Q and at right angles to the line joining P and Q. The distance RS is much greater than the distance PQ. Along which of the lines illustrated is an interference pattern observed?

Interference

A bar oscillates at frequency $f$ and generates water waves in a ripple tank. These waves then travel through a barrier that has a gap of width $x$, causing diffraction. Which pair of vibration frequency and gap width would give the least diffraction angle?

Diffraction

An ion is sped up in a vacuum by a sequence of electrodes. A graph is drawn of the power delivered to the ion against time. What quantity is shown by the area beneath the graph between two times?

Energy conservation

As shown in the diagram, a diffraction grating is employed to determine the wavelength of monochromatic light. The spacing of the slits in the grating is $1.00 \times 10^{-6}\,\text{m}$. The angle between the first order diffraction maxima is $70.0^\circ$. What is the wavelength of the light?

The diffraction grating

A small sphere with charge and mass $0.80\,\text{g}$ is suspended by a light thread in a vertical uniform electric field of magnitude $2000\,\text{V m}^{-1}$. The thread runs over two frictionless pulleys, and a mass of $2.00\,\text{g}$ is attached to the free end. The sphere is in equilibrium. What charge does the sphere carry?

Equilibrium of forces

An electron moves into a region of space containing a uniform electric field $E$, as illustrated. At the start, the electron is travelling parallel to the electric field and in the same direction as it. How will the electric field affect the electron’s path afterwards, and what happens to its speed?

Momentum and Newton's laws of motion

The current in the circuit diagram shown is $3.2\,\text{mA}$. What is the direction of electron flow through the resistor $R$, and what is their rate of flow?

Electric current

A filament lamp has a resistance of $180\,\Omega$ when the current through it is $500\,\text{mA}$. What power is dissipated by the lamp?

Potential difference and power

Copper wires X and Y each have the same volume. Wire Y is four times longer than wire X. What is the ratio $\dfrac{\text{resistance of wire Y}}{\text{resistance of wire X}}$?

Resistance and resistivity

In the circuit diagram shown, the ammeter shows $I$ and the voltmeter shows $V$. Once the switch is closed, which row states the effect on $I$ and on $V$?

Practical circuits

A cell with electromotive force $E$ and negligible internal resistance is joined to a resistor network containing resistances $R_1$, $R_2$, $R_3$ and $R_4$, as illustrated. The circuit branches carry currents $I_1$, $I_2$ and $I_3$. Which equation is correct?

Kirchhoff's laws

The circuit diagram contains four resistors with different resistances $P$, $Q$, $R$ and $S$ connected to a battery. The voltmeter shows zero. Which equation is correct?

Potential dividers

An astatine nucleus has a nucleon number of $218$ and a proton number of $85$. It undergoes decay to make a polonium nucleus, with a $\beta$-particle and an $\alpha$-particle emitted during the process. What are the nucleon number and the proton number of this polonium nucleus?

Atoms, nuclei and radiation

What is a typical value for the wavelength of a microwave moving through a vacuum?

Electromagnetic spectrum

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

Atoms, nuclei and radiation

A double-slit interference experiment is performed to find the wavelength of light from a monochromatic source. The measurements below are given: slit separation $a = 0.50 \pm 0.02\,\text{mm}$ fringe separation $x = 1.7 \pm 0.1\,\text{mm}$ distance between slits and screen $D = 2.000 \pm 0.002\,\text{m}$ What percentage uncertainty is there in the wavelength that is calculated?

Errors and uncertainties

With no air movement, a bird can move at a speed of $10\,\text{m s}^{-1}$. The wind is blowing from the east at $8.0\,\text{m s}^{-1}$. What direction should the bird head in so that it reaches a place that lies due north of its present position?

Scalars and vectors

An archer launches an arrow towards a target. The diagram illustrates the arrow's trajectory. Air resistance is taken to be negligible. The graphs indicate how three quantities $p$, $q$ and $r$, connected to the motion of the arrow, change with time. Which quantity represents the horizontal component of displacement, and which quantity represents the vertical component of displacement of the arrow?

Equations of motion

A hot-air balloon travelling vertically is subjected to three forces: its weight, the force from air resistance, and the upthrust force. The hot-air balloon is descending vertically at a constant speed. The air resistance force acting on the balloon is $F$. What weight of material must be released from the balloon so that it rises vertically at the same constant speed?

Momentum and Newton's laws of motion

A car travels along a straight path at constant speed, with the engine supplying a driving force that is equal to the resistive force $F$. After the engine is turned off, the car comes to rest over a distance of $100\,\text{m}$ because of the resistive force. You may assume that $F$ remains unchanged throughout the deceleration. The experiment is then carried out again using the same car with the same initial speed, but this time the resistive force is a constant $0.800F$. What distance does the car cover as it slows down?

Equations of motion

Which pair of units are not equivalent when written in SI base units?

SI units

Two blocks, with masses $M$ and $m$, are connected by a light string that goes over a frictionless pulley, as illustrated. The acceleration of free fall has magnitude $g$. What is the acceleration $a$ of the two blocks?

Momentum and Newton's laws of motion

The diagram depicts a block of copper hanging in water. The block is acted on by an upthrust from the water. Which statement provides the principle for explaining this upthrust?

Density and pressure

The diagram depicts a solid cube of weight $W$ and edge length $L$. It is held stationary by a frictionless spindle that goes through the centres of two opposite vertical faces. One of these faces is shaded. The spindle is then taken away and set back at a position $rac{L}{4}$ to the right of where it originally was. When the shaded face is being viewed, determine the torque of the couple that is now required to keep the cube stationary.

Turning effects of forces

A street lamp is attached to a wall using a metal rod and a cable. Which vector triangle could show the forces acting at point $P$?

Equilibrium of forces

As illustrated, two rigid steel beams $XY$ and $YZ$ have their lower ends fixed in position and are joined by a hinge at $Y$. Each beam is set at an angle of $50^\circ$ to the horizontal. A load of $4.0 \times 10^4\,\text{N}$ is suspended from $Y$. The system is in equilibrium. What force does each beam exert on the hinge at $Y$?

Equilibrium of forces

A quantity of air is enclosed in a glass bulb that is placed in water and connected to a U-tube filled with mercury. The densities of the water and the mercury are $\rho_w$ and $\rho_m$ respectively. The water surface is exposed to the atmosphere, where the atmospheric pressure is $P$. The acceleration of free fall is $g$. What is the pressure of the air in the glass bulb?

Density and pressure

A ball of mass $m$ is projected vertically upwards in air with an initial velocity $v$ to a height $h$, as illustrated. Air resistance may be ignored. The acceleration of free fall is $g$. What is the total work done by the gravitational force on the ball while it moves from $P$ to $Q$?

Gravitational potential energy and kinetic energy

A force $F$, constant in magnitude, acts on a car of mass $m$ and raises the car up a slope over a distance $s$ at constant velocity $v$. The slope is inclined at an angle $\alpha$ to the horizontal. What is the ratio $\frac{\text{gravitational potential energy gained by car}}{\text{work done by force } F}$?

Gravitational potential energy and kinetic energy

Car X is moving at half the speed of car Y. The mass of car X is twice the mass of car Y. Which statement is the correct one?

Momentum and Newton's laws of motion

As a petrol car is being refuelled, it receives $50$ litres of fuel in $90$ seconds. Each litre of petrol contains $34\,\text{MJ}$ of energy. If an electric car is to obtain the same total energy in the same period from a $230\,\text{V}$ supply, what minimum current is needed?

Potential difference and power

What is the component of this displacement vector in the vertical direction?

Scalars and vectors

A bolt is acted on by a tensile force, as illustrated. 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 $\frac{\text{stress at Y}}{\text{stress at X}}$?

Stress and strain

A rectangular steel block that holds up a very large bridge component has a height of $15\,\text{cm}$ and a cross-section measuring $20\,\text{cm} \times 12\,\text{cm}$. It is intended to shorten by $1\,\text{mm}$ when the maximum uniformly distributed load acts on it. The Young modulus of steel is $2.0 \times 10^{11}\,\text{N m}^{-2}$. Determine the greatest load it can carry.

Stress and strain

As sound moves through air, the air particles oscillate. A displacement-time graph for one air particle is shown. Which graph best represents how the kinetic energy of the air particle changes with time?

Transverse and longitudinal waves

Which type of wave is longitudinal?

Transverse and longitudinal waves

A vibrating tuning fork is positioned above a glass cylinder that has been filled to the top with water. The water level is then lowered at a constant rate. The first loud sound is detected when the water level is $83.5\,\text{cm}$ above the bench. The next loud sound is detected when the water level is $17.1\,\text{cm}$ above the bench. The speed of sound in air is $340\,\text{m s}^{-1}$. Calculate the frequency of the tuning fork.

Stationary waves

A train travelling along a railway track in a straight line has a whistle that emits sound continuously at frequency $f$. A woman standing beside the track hears a sound with frequency $0.85f$. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the train’s velocity?

Doppler effect for sound waves

A beam of orange light in a vacuum has wavelength $600\,\text{nm}$. What frequency does this light have?

Electromagnetic spectrum

A stationary sound wave contains a sequence of nodes. The separation between the first node and the sixth node is $30.0\,\text{cm}$. Determine the wavelength of the sound wave.

Stationary waves

Which diagram illustrates the diffraction of water waves in a ripple tank?

Diffraction

A hill lies between a radio transmitter and a house, as illustrated. The transmitter is not visible from the house, yet radio waves from it are detected at the house. Why does this happen?

Diffraction

The units of specific heat capacity are $\text{J kg}^{-1}\,\text{K}^{-1}$. Which SI base units correspond to specific heat capacity?

SI units

In an experiment showing double-slit interference with light, the slit-to-screen distance is doubled, and the slit separation is reduced to half. The wavelength of the light is unchanged. By what factor does the spacing between neighbouring bright fringes change?

Interference

In the diagram, two metal plates are joined to a constant high voltage. Which graph shows how the electric field strength $E$ halfway between the two plates changes as the separation $d$ between the two plates is increased?

Potential difference and power

An electron travels from point X to point Y through a uniform electric field, as illustrated. The separation between X and Y is $4.0\,\text{cm}$, and the line XY makes an angle of $60^\circ$ with the field direction. The field provides the only force acting on the electron. The magnitude of the field is $100\,\text{N C}^{-1}$. Determine the change in kinetic energy of the electron as it moves from X to Y?

Potential difference and power

Two copper wires are connected end to end and a current flows through them, as shown. Wire P has diameter $d$ and wire Q has diameter $2d$. What is the ratio $\displaystyle \frac{\text{average drift speed of the free electrons in wire P}}{\text{average drift speed of the free electrons in wire Q}}$?

Electric current

A cell with negligible internal resistance is connected to resistors $R_1$, $R_2$ and $R_3$, as illustrated. The cell supplies energy to the circuit, and energy is dissipated in the resistors. Which word equation must be correct?

Potential difference and power

Which graph shows a metallic conductor, with the resistance of the conductor being given by the gradient of the graph?

Resistance and resistivity

A typical mobile phone battery has an e.m.f. of $5.0\,\text{V}$ and an internal resistance of $200\,\text{m}\Omega$. What is the terminal p.d. of the battery when it delivers a current of $500\,\text{mA}$?

Practical circuits

In the circuit diagram, the resistor $S$ is connected so that it is neither in series with nor in parallel to the other resistors. Using Kirchhoff’s laws together with the information given in the diagram, it is possible to work out the resistance of each of the two identical resistors marked $R$. What is the resistance of each resistor $R$?

Kirchhoff's laws

The diagram illustrates a potential divider linked to a $12\,\text{V}$ supply with negligible internal resistance. Which range of voltages may be produced between X and Y?

Potential dividers

The diagram represents a chain of radioactive decays that includes three $\alpha$-particles and one $\beta^-$ particle. $^{237}_{93}\text{Np} \xrightarrow{\alpha} Q \xrightarrow{\beta^-} R \xrightarrow{\alpha} S \xrightarrow{\alpha} T$ Which nuclide is T?

Atoms, nuclei and radiation

The equation below defines a quantity $y$ that must be found. $y = \dfrac{p x}{q^2}$ The percentage uncertainties for $p$, $x$ and $q$ are given below. $p$: $6\%$ $x$: $2\%$ $q$: $4\%$ What is the percentage uncertainty in $y$?

Errors and uncertainties

Which pairing of up (u) and down (d) quarks makes up a neutron?

Fundamental particles

A transmitter sends a pulse of electromagnetic waves towards a reflector. The pulse is reflected back and reaches the transmitter again. A detector is placed at the transmitter. The outgoing pulse and the reflected pulse are shown on a cathode-ray oscilloscope (c.r.o.) as shown. The pulse takes $6.3\,\mu\text{s}$ to travel from the transmitter to the reflector. What is the time-base setting of the c.r.o.?

Practical circuits

A hot-air balloon is travelling vertically upward at a steady speed of $3.00\,\text{m s}^{-1}$. A sandbag is released from the balloon. It takes $5.00\,\text{s}$ for the sandbag to reach the ground. How high was the balloon when the sandbag was let go?

Equations of motion

The velocity-time graph for a train that sets off from one station and comes to a halt at the next station is shown. A second train has twice the acceleration, but it has the same maximum speed and the same deceleration. Which velocity-time graph, using the same scale, represents the motion of this train between the same stations?

Equations of motion

A stone is let go from rest and drops through a large distance in air. Which graph might represent how the acceleration $a$ of the stone changes with time $t$?

Non-uniform motion

A slow-moving vehicle and a fast-moving vehicle head straight towards one another and then collide. Which result can never happen, no matter what the masses of the vehicles are?

Linear momentum and its conservation

How many cubic nanometres, $\text{nm}^3$, are contained in one cubic micrometre, $\mu\text{m}^3$?

SI units

Two railway trucks with masses $m$ and $3m$ are travelling towards one another in opposite directions at speeds $2v$ and $v$ respectively. The trucks collide and join together. What is the speed of the trucks after the collision?

Linear momentum and its conservation

A stone is projected horizontally in a vacuum and follows the path shown. X is a point on this path. XV and XH are vertical and horizontal lines respectively through X. XT is the tangent to the path at X. In which directions do forces act on the stone at X?

Momentum and Newton's laws of motion

Two forces, each of magnitude $F$, act along the sides of a rectangular metal plate, as illustrated. The plate has length $a$ and width $b$. What is the torque about point P?

Turning effects of forces

A solid sphere moves down through a liquid at constant (terminal) velocity. The diagram shows the three forces acting on the sphere. What is the relationship between these three forces?

Equilibrium of forces

A flat, thin plate with area $0.036\,\text{m}^2$ lies below the surface of a liquid of density $930\,\text{kg m}^{-3}$. The force on one face of the plate caused by the liquid pressure is $290\,\text{N}$. How far beneath the liquid surface is the plate?

Density and pressure

A ball is projected straight up vertically. Air resistance is negligible. Which of the following statements is correct?

Equations of motion

A car with a total mass of $1560\,\text{kg}$ moves at a steady speed of $32\,\text{m s}^{-1}$. The car provides a driving force of $680\,\text{N}$. Its kinetic energy is $800\,\text{kJ}$ and its momentum is $50\,000\,\text{N s}$. Which two pieces of data could be used to work out the useful power output of the car?

Energy conservation

A horizontal cylinder with cross-sectional area $A$ is equipped with a frictionless piston and contains air at pressure $P$. It is placed in hot water, causing the length of the air column to rise from $x$ to $y$. The pressure $P$ stays constant. Which equation shows the work done by the trapped air during this process?

Density and pressure

A trolley moves across a level surface, then goes up an incline before arriving on a second level surface. The incline has length $L$. The trolley’s mass is $M$. The incline makes an angle $\alpha$ with the horizontal surface. The second horizontal surface is at height $h$ above the first surface. Ignore frictional forces. The acceleration of free fall is known. To find the minimum initial velocity needed for the trolley to just reach the top of the slope, what further quantities are required?

Gravitational potential energy and kinetic energy

The diagram indicates an arrangement that is used to determine the output power of an electric motor. The wheel fitted to the motor’s axle has a circumference of $0.5\,\text{m}$, and the belt passing over it remains stationary when the weights have the values shown. If the wheel is turning at $20$ revolutions per second, what is the output power of the motor?

Energy conservation

The greatest theoretical power $P$ for a wind turbine is described by the equation $P = k\rho A v^n$, in which $\rho$ represents the density of air, $A$ is the area swept out by the turbine blades, $v$ is the speed of the air and $k$ is a constant with no units. What is the value of $n$?

SI units

A piece of metal is acted on by a force that rises to a maximum value and then returns to zero. A force-extension graph for the piece is shown. As the piece contracts, it retraces the same force-extension curve as during stretching. What behaviour does the metal show between $X$ and $Y$?

Elastic and plastic behaviour

A load is suspended from the end of a metal wire. The load is then increased and the wire extends elastically. The table gives the length of the wire for different loads. When the load is $4.0\,\text{kN}$, what is the strain energy stored in the wire?

Elastic and plastic behaviour

The graph illustrates the way a particle’s displacement in a wave changes with time. Which statement is correct?

Progressive waves

A wave moves along a coiled spring. The graph shows how the displacement of one point on the spring changes with time. What is the wave frequency?

Progressive waves

An electrical signal is shown on a cathode-ray oscilloscope (c.r.o.). The time-base is adjusted to $50\,\text{ms div}^{-1}$. The Y-gain is adjusted to $2\,\text{V div}^{-1}$. What is the amplitude of the signal?

Practical circuits

A sound source with frequency $F$ at point $Z$ is travelling at a constant speed. The arrangement of the wavefronts it emits is shown. Which row gives the frequencies of the sound detected by stationary observers at $X$ and $Y$?

Doppler effect for sound waves

A car is moving in a straight line at constant speed and passes near a stationary observer. The observer records the frequency of the sound produced by the engine. When the car is coming towards the observer, the measured frequency is $220\,\text{Hz}$. When the car is travelling away, the measured frequency is $180\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. What is the speed of the car?

Doppler effect for sound waves

Which frequency of electromagnetic radiation might be ultraviolet?

Electromagnetic spectrum

An electromagnetic wave moves in a straight line through a vacuum. Its frequency is $6.0\,\text{THz}$. How many wavelengths are contained in a distance of $1.0\,\text{m}$ measured along the wave?

Progressive waves

A narrow slit is illuminated by a beam of laser light. Once it passes through the slit, the light strikes a screen. What pattern of light is observed on the screen?

Diffraction

What is the horizontal component of the force shown in the diagram?

Scalars and vectors

The diagrams depict four pairs of waves. For each pair, the displacement $y$ at a fixed point is plotted against time $t$. Which pair of waves is not coherent?

Interference

The diagram illustrates the electric field around a positively charged sphere and a negatively charged sphere. Four electrons $A$, $B$, $C$ and $D$ are placed at different points in the field. For which electron is the direction of the force on the electron indicated correctly?

Scalars and vectors

Lightning may form between a charged cloud and the Earth’s surface once the electric field strength in the air between them reaches $25\,\text{kN C}^{-1}$. The diagram illustrates the electric field from the base of a cloud to the Earth’s surface. Calculate the smallest potential difference between the Earth and the base of a cloud, $2.0\,\text{km}$ high, needed for lightning to happen?

Potential difference and power

The conduction-electron number density in copper is $8.0 \times 10^{28}\,\text{m}^{-3}$. For a copper wire with diameter $0.42\,\text{mm}$ carrying a current of $0.57\,\text{A}$, what is the mean drift speed of the electrons?

Electric current

A straightforward circuit consists of a source of electromotive force (e.m.f.) linked to a load. In what way does the source’s output power $P$ vary with the source’s internal resistance $r$ and the load resistance $R$?

Potential difference and power

For an ideal diode, the resistance is zero when it is forward biased and infinite when it is reverse biased. The diode is placed in series with a $2\,\Omega$ resistor across the terminals of a source with electromotive force (e.m.f.) $3\,\text{V}$ and internal resistance $1\,\Omega$, as shown. A voltmeter with very high resistance is connected across the diode and resistor. Which row shows the voltmeter readings for the two possible ways of connecting the diode?

Practical circuits

A resistor $R$ is joined in series with two cells, each of electromotive force (e.m.f.) $E$ but with different internal resistances $r_1$ and $r_2$. The voltmeter reading is $0\,\text{V}$. What is the resistance of $R$?

Kirchhoff's laws

There are three identical cells, each with electromotive force (e.m.f.) $E$ and negligible internal resistance. As shown, the cells are linked to three identical resistors, each of resistance $R$. What potential difference is there between P and Q?

Kirchhoff's laws

For each resistor arrangement, the ammeter has a resistance of $2\,\Omega$. Which arrangement produces the highest ammeter reading if the same potential difference is applied across points P and Q?

Practical circuits

In each option, the table gives the numbers of neutrons, protons and electrons in two atoms, some of which are ions. Which pair of atoms in the table are isotopes of the same element?

Atoms, nuclei and radiation

A school uses a sheet of aluminium in radioactivity experiments. Its thickness is labelled as $3.2\,\text{mm}$. A student chooses to verify this value. He has vernier calipers that measure to $0.1\,\text{mm}$ and a micrometer that measures to $0.01\,\text{mm}$. Which statement must be correct?

Errors and uncertainties

What combination of up (u) and down (d) quarks makes up a proton?

Fundamental particles

Four possible causes of error in a set of measurements are given below. 1 an analogue meter that is viewed from different angles when its scale is read 2 a meter that consistently gives readings $5\%$ too high 3 a meter with a needle that is not frictionless, so the needle occasionally sticks a little 4 a meter that has a zero error Which errors are random and which are systematic?

Errors and uncertainties

A football drops from the top of a tall building. Which graph most accurately shows how the distance $x$ fallen changes with time $t$?

Equations of motion

Two identical cars P and Q are moving along a straight road. Car Q is travelling at twice the speed of car P. The brakes are then applied to both cars, causing the same constant deceleration. Which graph illustrates how the velocity $v$ of each car changes with time $t$?

Equations of motion

A man is in a lift that is accelerating downward vertically, as shown. Which statement describes the force that the man exerts on the floor?

Momentum and Newton's laws of motion

A snooker ball with a mass of $200\,\text{g}$ strikes the cushion of a snooker table at right angles, moving at a speed of $14.0\,\text{m s}^{-1}$. It bounces back with one half of its original speed. The ball remains in contact with the cushion for $0.60\,\text{s}$. What is the average force exerted on the ball by the cushion?

Momentum and Newton's laws of motion