May/June 2017

A student produces a table giving sensible estimates for several physical quantities. Which row is not a sensible estimate?

Physical quantities

The graph illustrates the way the momentum of a motorcycle varies with time. What is the resultant force on the motorcycle?

Momentum and Newton's laws of motion

A particle that has mass and charge is travelling from left to right through a uniform gravitational field and a uniform electric field. The gravitational field acts downwards. On this particle, the gravitational force and the electric force act in opposite directions. What could the sign of the charge on the particle be, and what is the direction of the electric field?

Potential difference and power

A sphere is acted on by several forces, each with the same magnitude. Which arrangement of forces produces a resultant torque but no resultant force on the sphere?

Turning effects of forces

A horizontal footbridge of uniform density has a length of $12\,\text{m}$ and a weight of $4000\,\text{N}$. It is supported at two points, X and Y, as illustrated. A man whose weight is $600\,\text{N}$ stands $4\,\text{m}$ from support X. What upward force does support X exert on the footbridge?

Equilibrium of forces

A metal block has a mass of 750 g. 60% of its mass is magnesium, and the rest is copper. The density of magnesium is $1.7\,\text{g cm}^{-3}$. The density of copper is $9.0\,\text{g cm}^{-3}$. What is the density of the block?

Density and pressure

A man ascends a ladder at a constant, slow pace. What is the principal energy transfer occurring for the man while he climbs?

Gravitational potential energy and kinetic energy

Over a period of time, fuel provides energy $X$ to a car. As the car speeds up, part of this energy is changed into kinetic energy. The remaining energy $Y$ is transferred away as thermal energy. Find the efficiency of the car.

Energy conservation

A railway engine increases the speed of a train with a total mass of 800 tonnes (1 tonne = 1000 kg) from rest until it reaches $50\,\text{m s}^{-1}$. What amount of useful work has to be carried out on the train for it to attain this speed?

Gravitational potential energy and kinetic energy

A mass is lifted vertically upward. Over time $t$, its gravitational potential energy increases by $E_p$ and its kinetic energy increases by $E_k$. What is the average power supplied to the mass?

Energy conservation

Water passes from a lake to a turbine positioned a vertical distance of $90\,\text{m}$ beneath the lake surface, as illustrated. The water’s mass flow rate is $2400\,\text{kg min}^{-1}$. The turbine operates with an efficiency of $75\%$. Calculate the output power of the turbine.

Gravitational potential energy and kinetic energy

A particle moves along a straight line with speed $v$. The particle decelerates and then changes direction. Its new speed is $\frac{v}{2}$. The new velocity has a component of $\frac{v}{4}$ in the same direction as the particle's original path. Through what angle has the particle turned?

Scalars and vectors

A wire with diameter $d$ and length $l$ is suspended vertically from a fixed support. By attaching a mass $M$ to its lower end, the wire is stretched. The Young modulus of the wire is $E$. The acceleration of free fall is $g$. Which equation is used to find the extension $x$ of the wire?

Stress and strain

The graph shows how the compression of a spring changes as the force on it increases. A block is moving along a level surface with no friction towards the spring, as illustrated. The spring stops the block. Once the spring has been compressed by $4.0\,\text{cm}$, the block’s entire kinetic energy has been converted into elastic potential energy in the spring. What is the kinetic energy of the block at the moment it first touches the spring?

Energy conservation

A longitudinal wave passes along a long spring. The spring is illustrated at a particular moment. What is the wavelength of the wave?

Progressive waves

A sound wave moves with speed $1500\,\text{m s}^{-1}$ and frequency $2500\,\text{Hz}$. Find the smallest separation between a point of maximum pressure in the wave and a point of minimum pressure.

Progressive waves

The display on a cathode-ray oscilloscope (c.r.o.) shows a sound wave, as illustrated. The c.r.o. time-base is adjusted to $2.5\,\text{ms cm}^{-1}$. What is the frequency of this sound wave?

Progressive waves

A car moving along a straight path at a speed of $30\,\text{m s}^{-1}$ passes a stationary observer while its horn is sounding. The actual frequency of the sound from the horn is $400\,\text{Hz}$. The speed of sound in air is $336\,\text{m s}^{-1}$. What is the change in the frequency of the sound heard by the observer as the car goes past?

Doppler effect for sound waves

Which sequence lists electromagnetic waves in order of rising frequency?

Electromagnetic spectrum

The diagram depicts a steel wire fixed at one end. At the free end, a weight is hanging from the wire over a pulley. A vibrator is fitted to the wire close to the fixed end. A stationary wave containing one loop is formed. The vibrator operates at frequency $f$. Which frequency should be chosen to form a stationary wave with two loops?

Stationary waves

A parallel beam of light with wavelength $600\,\text{nm}$ is directed at right angles onto a diffraction grating. The grating contains $300$ lines per millimetre. What is the total number of intensity maxima produced by the grating?

The diffraction grating

An interference fringe pattern is formed with a red laser, a double slit and a screen. The screen is located $3.5\,\text{m}$ away from the double slit. The laser light has a wavelength of $640\,\text{nm}$. The fringe pattern is shown. What is the slit separation?

Interference

The speed $v$ at which a liquid exits a tube is affected by the pressure change $\Delta P$ and the liquid density $\rho$. This speed is described by $v = k \left( \frac{\Delta P}{\rho} \right)^n$ where $k$ is a constant with no units. What is the value of $n$?

Density and pressure

The diagram shows two points P and Q positioned $90^\circ$ apart on a circle with radius $r$. A positive point charge at the centre of the circle produces an electric field of magnitude $E$ at both P and Q. Which expression gives the work done when a unit positive charge is moved from P to Q?

Potential difference and power

The diagram depicts two horizontal metal plates arranged in parallel. The upper plate carries positive charge, while the lower plate is earthed. A tiny charged liquid drop, positioned halfway between the plates, remains in equilibrium because its weight is balanced by the electric force acting on it. The acceleration of free fall is $g$ and the electric field strength is $E$. What polarity does the charge on the drop have, and what is the ratio of charge to mass of the drop?

Potential difference and power

The diagram illustrates the symbol for a wire through which a current $I$ flows. What is meant by this current?

Electric current

Which combination of current and resistance would give an energy transfer rate of $16\,\text{J s}^{-1}$?

Potential difference and power

Which component is represented by the $I$-$V$ graph shown?

Resistance and resistivity

The circuit diagram shows a cell with constant internal resistance together with an external resistor $R$. A student notes the ammeter and voltmeter readings. She then adds a second external resistor identical to the first and connects it in parallel with the first external resistor. What change occurs in the ammeter reading and in the voltmeter reading?

Practical circuits

A computer is being used to sense when a switch changes position. To detect the change in position, the computer needs a potential difference (p.d.) of $0\,\text{V}$ at its input for one switch position and a p.d. between $5\,\text{V}$ and $7\,\text{V}$ for the other switch position. In each circuit, take the battery to have negligible internal resistance. Which circuit gives an input voltage to the computer that allows it to detect the switch’s change of position?

Potential dividers

In the circuit diagram, the battery and ammeter have negligible resistance. Each of the resistor combinations below is placed separately between terminals $X$ and $Y$ in the circuit. Which combination would result in an ammeter reading of $8\,\text{A}$?

Practical circuits

The table gives the nucleon number and the proton number for different nuclei. The nuclei are labelled $L$ to $T$. Which row in the table below shows correctly three nuclei of the same element, and three nuclei with the same number of neutrons?

Atoms, nuclei and radiation

A radioactive nucleus is created by $\beta^{-}$ decay. It then undergoes $\alpha$-emission. Which graph of nucleon number $N$ against proton number $Z$ represents the $\beta^{-}$ decay followed by the $\alpha$-emission?

Atoms, nuclei and radiation

The values of a vehicle’s displacement, velocity and acceleration can be worked out from graphs showing its motion. In many cases, either the area under these graphs or the gradient of the graphs is used. What would not provide a value for a displacement, a velocity or an acceleration?

Non-uniform motion

How are the proton and the neutron structured in terms of quarks?

Fundamental particles

A ball is dropped from rest above a rigid, horizontal surface. The graph shows how the velocity of the bouncing ball changes with time. At what point on the graph does the ball attain its greatest height after the first bounce?

Equations of motion

A ball is projected upward at an angle of $45^{\circ}$ above the horizontal ground. After a brief flight, the ball lands back on the ground. Assume that air resistance can be neglected. What quantity is never zero during the ball’s flight?

Equations of motion

A rocket-propelled truck has a mass that is roughly the same as the mass of the fuel stored in its tank. The fuel is set alight, and a constant force drives the truck along horizontal tracks. Air resistance can be ignored. In a test run, the fuel is used up at a steady rate. Which statement describes how the acceleration of the truck changes during the test run?

Momentum and Newton's laws of motion

At time $t = 0$, an object is released from a tall building. Air resistance is significant. Three graphs are drawn with time on the horizontal axis: - the object's height above the ground - the object's speed - the magnitude of the resultant force acting on the object Which quantities are X, Y and Z?

Non-uniform motion

A student is trying to determine the density $\rho$ of aluminium by measuring a rectangular sheet. mass $m = 51.6 \pm 0.1\,\text{g}$ length $l = 100.0 \pm 0.1\,\text{cm}$ width $w = 10.0 \pm 0.1\,\text{cm}$ thickness $t = 0.20 \pm 0.01\,\text{mm}$ He applies the equation $\rho = \frac{m}{wlt}$ to calculate the density. What is the density value obtained, together with its uncertainty?

Errors and uncertainties

What is the approximate mean speed of a female Olympic winner in a $100\,\text{m}$ race?

Physical quantities

A metal cylinder hangs vertically at rest, supported by a cord. The diagram shows the cylinder in four separate positions P, Q, R and S. Which statement accounts for the change in the tension $T$ in the cord?

Equilibrium of forces

In a machine, several couples act on a rotating object, as shown. What is the net torque acting on the rotating object?

Turning effects of forces

A uniform beam is pivoted at $P$ as shown. A $10\,\text{N}$ weight and a $20\,\text{N}$ weight are fixed to the two ends. The beam is graduated in $0.1\,\text{m}$ intervals. The beam itself has a weight of $100\,\text{N}$. At which point should an additional $20\,\text{N}$ weight be placed so that the beam is in equilibrium?

Turning effects of forces

State the SI base units for the quantity $\dfrac{\text{pressure}}{\text{density}}$?

SI units

In an inelastic collision, which quantities remain conserved?

Linear momentum and its conservation

A cyclist moves up a hill at a steady speed. The frictional force opposing the cyclist’s motion is $8.0\,\text{N}$. The cyclist uses $450\,\text{J}$ of energy to cover a distance of $20\,\text{m}$. What is the increase in the cyclist’s gravitational potential energy?

Energy conservation

A stone with mass $m$ drops from rest from the top of a cliff of height $h$ into the sea beneath. Immediately before reaching the sea, the stone has speed $v$. What is the average force of air resistance acting on the stone while it falls?

Energy conservation

A railway engine speeds up a train with a total mass of $1200$ tonnes ($1\,\text{tonne} = 1000\,\text{kg}$), taking it from rest to $75\,\text{m s}^{-1}$. How much useful work has to be done on the train for it to reach this speed?

Gravitational potential energy and kinetic energy

Which derivation of the equation connecting power, force and velocity is correct?

Energy conservation

A cable in a suspension bridge carries a load of $19.3 \times 10^5\,\text{N}$. Under this load, the cable extends by $47\,\text{mm}$. When a lorry then travels across the bridge, the force on the cable rises to $23.3 \times 10^5\,\text{N}$. The force-extension graph for the cable is shown. What is the increase in strain energy in the cable when the lorry is crossing the bridge?

Elastic and plastic behaviour

Two forces are acting on a circular disc, as illustrated. Which diagram shows the line of action of the resultant force?

Turning effects of forces

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

Stress and strain

A rubber band is pulled out and then allowed to return to its original length. The diagram gives the force-extension graph for this sequence. When the force is increased, the graph goes along OPQ to extension $e$. When the force is decreased, the graph goes along QRO to come back to zero extension. The area marked $X$ lies between the curves OPQ and QRO. The area marked $Y$ is enclosed by the curve QRO and the horizontal axis. Which statement about the process is correct?

Elastic and plastic behaviour

An electromagnetic wave has a period of $1.0\,\text{ns}$. What are its frequency and wavelength?

Electromagnetic spectrum

Which statement concerning progressive longitudinal waves is incorrect?

Transverse and longitudinal waves

A bicycle gear wheel is a disc with 50 ‘teeth’ spaced evenly around its rim. It turns 10 times every second. As the wheel spins, a springy metal strip is made to vibrate by the passing ‘teeth’. The sound produced by the metal strip has a frequency equal to the strip’s vibration frequency. The speed of sound in air is $330\,\text{m s}^{-1}$. What wavelength does the emitted sound have?

Progressive waves

An ambulance is moving along a straight road at a speed of $30.0\,\text{m s}^{-1}$. The siren on the ambulance produces sound with a frequency of $2000\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. As the ambulance goes past a man who is standing at the roadside, what frequency does he hear while the ambulance is approaching him, and what frequency does he hear while it is moving away from him?

Doppler effect for sound waves

The frequencies of three separate electromagnetic waves, P, Q and R, are listed as follows: $P = 3 \times 10^{10}\,\text{Hz}$, $Q = 3 \times 10^{13}\,\text{Hz}$, $R = 6 \times 10^{14}\,\text{Hz}$. Which row correctly identifies P, Q and R?

Electromagnetic spectrum

Which row shows the oscillations of two moving particles in a stationary wave when they are separated by half a wavelength?

Stationary waves

A parallel beam of red light with wavelength $700\,\text{nm}$ falls perpendicularly on a diffraction grating with 400 lines per millimetre. What is the total number of intensity maxima produced by the grating?

The diffraction grating

Two wave sources vibrate in phase. Each source emits a wave with wavelength $\lambda$. At point X, the two waves arriving from the sources have a phase difference of $90^{\circ}$. What is one possible difference between the distances from the two wave sources to point X?

Interference

Which expression correctly represents the volt in SI base units?

Potential difference and power

Which diagram most accurately shows the electric field surrounding a positive point charge?

Scalars and vectors

The trajectory of an electron, moving initially at speed $v$, in the uniform electric field between two parallel plates is illustrated. The vertical deflection $x$ is taken at the right-hand edge of the plates. The separation between the plates is reduced by half. The potential difference across the plates stays unchanged. What is the new deflection of the electron if it still starts with the same speed $v$?

Potential difference and power

The current through a circuit component is $2.00\,\mu\text{A}$. How many electrons pass through the component in each second?

Electric current

A filament in a $240\,\text{V}$, $100\,\text{W}$ electric lamp is heated from room temperature to its working temperature. During this warming, its resistance increases by a factor of 16. What is the resistance of the filament at room temperature?

Potential difference and power

Two wires have equal lengths and equal resistances. Wire X is formed from a metal with resistivity $1.7 \times 10^{-8}\,\Omega\,\text{m}$, and wire Y is formed from a metal with resistivity $5.6 \times 10^{-8}\,\Omega\,\text{m}$. The diameter of wire X is $0.315\,\text{mm}$. What diameter does wire Y have?

Resistance and resistivity

A cell has a constant electromotive force. A variable resistor is placed across the terminals of the cell. The resistance of the variable resistor is reduced. Which statement correctly describes how the cell’s terminal potential difference (p.d.) changes?

Practical circuits

Four resistors are arranged in a square, as illustrated. The resistance can be measured between any pair of junctions. Between which two junctions does the measured resistance have the greatest value?

Kirchhoff's laws

A circuit is arranged as shown. The variable resistor is altered so that the ammeter reading falls. What happens to the voltmeter readings?

Practical circuits

In a television programme used to demonstrate scientific models, a presenter repeatedly fires a gun at a bale of hay. Inside the hay, two small cannon balls are lodged some distance apart. The hay bale is about $2\,\text{m} \times 2\,\text{m} \times 2\,\text{m}$ in size, and the cannon balls are iron, nearly spherical, and roughly $5\,\text{cm}$ across. What is the presenter likely to be showing?

Atoms, nuclei and radiation

One particular nuclide, uranium-235, has nucleon number $235$, proton number $92$ and neutron number $143$. Information about four other nuclides is shown below. Which nuclide is an isotope of uranium-235?

Atoms, nuclei and radiation

A semiconductor block carries a current of $30.0\,\text{mA}$ when the potential difference (p.d.) across it is $10.0\,\text{V}$. The block’s dimensions and the direction of current flow are shown. The electrical meters used have accuracies of $\pm 0.1\,\text{mA}$ and $\pm 0.1\,\text{V}$. The block dimensions are accurate to $\pm 0.2\,\text{mm}$. What is the resistivity of the semiconductor?

Resistance and resistivity

In $\beta^-$ decay, what alteration occurs in the quark composition of the nucleus that releases the $\beta^-$ particle, and what other particle is emitted?

Atoms, nuclei and radiation

A micrometer screw gauge is used to measure the diameter of a cylindrical metal rod. The diagram below gives an enlarged view of the micrometer screw gauge scale while the measurement is being taken. What is the cross-sectional area of the rod?

Physical quantities

A ball is started moving at P on a frictionless surface. It travels upward along slope PQ, continues over the level section QR and then moves down slope RS. Which graph could show how the ball’s speed $v$ varies with time $t$ as the ball travels from P to S?

Non-uniform motion

A rubber ball is released so that it falls onto a table and then rebounds upward. The table applies a force $F$ to the ball. Which graph most accurately represents how the force $F$ changes with time $t$ during the brief interval when the ball is touching the table?

Momentum and Newton's laws of motion

A golf ball with mass $m$ is released from rest and falls onto a hard surface from height $h_1$, then bounces up to height $h_2$. The momentum of the golf ball immediately before it hits the surface is not the same as its momentum immediately after it leaves the surface. What is the total change in momentum of the golf ball during the interval between these two moments? (Ignore air resistance.)

Momentum and Newton's laws of motion

A book of weight $W$ is resting on a table. A student tries to describe Newton’s third law of motion by saying that ‘action equals reaction’. If the book’s weight is treated as the ‘action’ force, what is the ‘reaction’ force?

Momentum and Newton's laws of motion

What is the most suitable estimate for the kinetic energy of a family car moving at $50\,\text{km h}^{-1}$?

Gravitational potential energy and kinetic energy

A puck used in ice hockey, with a mass of $150\,\text{g}$, is travelling at an initial speed of $2.0\,\text{m s}^{-1}$ over the ice-rink surface. It then glides $30\,\text{m}$ in a straight path before coming to rest. What average frictional force acts on the puck?

Energy conservation

A uniform beam with mass $1.4\,\text{kg}$ is mounted on a pivot at $P$, as illustrated. The beam is $0.60\,\text{m}$ long, and $P$ lies $0.20\,\text{m}$ from one end. Masses of $3.0\,\text{kg}$ and $6.0\,\text{kg}$ are hung $0.35\,\text{m}$ and $0.15\,\text{m}$ from the pivot, as shown. What torque must be applied to the beam so that it stays in equilibrium?

Turning effects of forces

A bubble of air moves upwards through a liquid with a constant speed. The forces acting on it are the upthrust $U$, the viscous drag $D$ and its weight $W$. Which diagram shows the directions of these forces and their relative sizes?

Equilibrium of forces

The diagram shows a sphere submerged in water. $P$, $Q$, $R$ and $S$ are forces on the sphere caused by the water pressure. Each force acts at right angles to the sphere’s surface. $P$ and $R$ act vertically in opposite directions. $Q$ and $S$ act horizontally in opposite directions. Which statement about the sizes of the forces is correct?

Density and pressure

The table’s first column shows four examples of work in progress. The second column provides extra detail about the action. Which row is incorrect?

Energy conservation

A steam turbine is used to turn a generator. The power entering the turbine is $P_I$, and the power leaving it is $P_O$. The power lost in the turbine is $P_L$, as shown. What is the efficiency of the turbine?

Energy conservation

A constant force acts on a block, driving it across a horizontal surface with no friction. Starting from rest, the block travels a fixed distance. What is the connection between the block’s final speed $v$ and its mass $m$?

Equations of motion

A man of mass $80\,\text{kg}$ attaches himself to one end of a rope that passes over a single fixed pulley. He pulls the free end of the rope so that he rises with an average speed of $50\,\text{cm s}^{-1}$. What is the average useful power at which he is working?

Gravitational potential energy and kinetic energy

There are two wires that have the same Young modulus $E$ and cross-sectional area $A$, although their lengths $L$ are different, and each wire is acted on by a different tensile force $F$. The extension $e$ of both wires is equal. The table headings list four separate quantities. Which of these quantities have equal values, and which have unequal values, for the two wires?

Stress and strain

Two springs $X$ and $Y$ undergo elastic extension. The graphs illustrate how the force $F$ applied to each spring changes with extension $x$. Which of the following statements is correct?

Elastic and plastic behaviour

The figure presents two vectors $X$ and $Y$. These vectors are at right angles to each other. Vector $X$ has magnitude $8.0\,\text{N}$, while vector $Y$ has magnitude $6.0\,\text{N}$. What are the magnitude and direction of vector $(X - Y)$?

Scalars and vectors

The diagram illustrates the force-extension graph for a steel wire, right up to the point at which it breaks. What is the best estimate of the work done in breaking the wire?

Elastic and plastic behaviour

Which of the following statements about electromagnetic waves in a vacuum is correct?

Electromagnetic spectrum

A transverse wave moves along a rope. The graph illustrates how the particles’ displacement varies with distance along the rope at one particular moment. At what distance along the rope do the particles have the greatest upward velocity?

Progressive waves

A trace appears on the screen of a cathode-ray oscilloscope (c.r.o.). The time-base setting is $2.5\,\text{ms cm}^{-1}$ and the Y-gain is $2.0\,\text{V cm}^{-1}$. Determine the frequency and the amplitude of the waveform shown on the c.r.o.?

Practical circuits

A stationary observer is approached by a high-speed train travelling at a speed of $80\,\text{m s}^{-1}$. The horn on the train produces a sound with frequency $250\,\text{Hz}$. The speed of sound is $340\,\text{m s}^{-1}$. What frequency is observed from the horn?

Doppler effect for sound waves

Which row gives the correct frequency in Hz for each of the four principal radiations?

Electromagnetic spectrum

A pipe with a length of $100\,\text{cm}$ is open at both ends. A loudspeaker placed at one end of the pipe is able to produce sound with different wavelengths. For which wavelength will a stationary wave be formed in the pipe?

Stationary waves

Monochromatic light falls on a diffraction grating, producing a diffraction pattern. Which row gives the possible effects of changing to a grating with twice as many lines per millimetre?

The diffraction grating

Monochromatic light with wavelength $\lambda$ falls on two narrow slits $S_1$ and $S_2$, separated by a small distance. A sequence of bright and dark fringes appears on a screen far from the slits. The $n$th dark fringe away from the central bright fringe is seen at point P on the screen. Which equation is true for every positive value of $n$?

Interference

A dipole consists of two charges with equal magnitude, one positive and the other negative. The electric field pattern for a dipole is shown. In which direction does the force act on an electron at point X?

Scalars and vectors

Which expression, written in SI base units, is equivalent to the volt?

SI units

In a uniform electric field, which statement is true?

Potential difference and power

Two metal plates are separated by a distance of $30\,\text{cm}$ in a vacuum. A current flows between the plates because electrons move at a steady speed of $1.5 \times 10^{6}\,\text{m s}^{-1}$. At every moment, only one electron is present in transit between the plates. What is the current between the plates?

Electric current

The diagram depicts a portable generator linked via cables to floodlights. The generator supplies a current of $10\,\text{A}$ at a fixed potential difference (p.d.) of $240\,\text{V}$. The combined resistance of the cables is $2\,\Omega$. What are the p.d. $V$ across, and the power $P$ delivered to, the floodlights?

Potential difference and power

A metal cube whose side length is $a$ has an electrical resistance of $R$ measured across opposite faces. What is the resistance across the opposite faces of another cube made of the same metal, but with side length $3a$?

Resistance and resistivity

The graph shown plots potential difference (p.d.) $V$ across a cell against the current $I$ in the cell. When the cell is close to the end of its useful life, its internal resistance rises and its electromotive force (e.m.f.) falls. Which diagram shows a graph of $V$ against $I$ for the cell nearing the end of its useful life?

Practical circuits

A $20\,\text{V}$ d.c. supply is connected to a circuit made up of five resistors $L$, $M$, $N$, $P$ and $Q$. A potential drop of $7\,\text{V}$ occurs across $L$, and there is an additional $4\,\text{V}$ potential drop across $N$. What potential drops are across $M$, $P$ and $Q$?

Kirchhoff's laws

A potential divider circuit is made up of a cell with negligible internal resistance connected in series with two variable resistors of resistances $R_1$ and $R_2$. The potential difference (p.d.) across the cell is $V_0$. The output p.d. is $V$. Which statement is correct?

Potential dividers

A nucleus of uranium-238, $^{238}_{92}\text{U}$, undergoes a decay chain in successive stages to produce a nucleus of lead-206, $^{206}_{82}\text{Pb}$, as illustrated. $^{238}_{92}\text{U} \;\rightarrow\; \ldots\ldots\ldots\ldots\; \rightarrow\; ^{206}_{82}\text{Pb}$ In each stage, either an $\alpha$-particle or a $\beta^-$ particle is emitted. What is the overall number of $\beta^-$ particles emitted?

Atoms, nuclei and radiation

Which statement concerning $\alpha$-particles is correct?

Atoms, nuclei and radiation

The nuclear equation below is incomplete. $^{14}_{6}\text{C} \;\rightarrow\; ^{14}_{7}\text{N} + ^{0}_{-1}\beta + \ldots\ldots\ldots\ldots$ What does the missing term represent?

Atoms, nuclei and radiation

A voltage is measured precisely using a reliable instrument and the result is $2.321\,\text{V}$. Two students, working by two different methods, state that the voltage is $2.33\,\text{V}$ and $2.344\,\text{V}$ respectively. Which statement is correct?

Errors and uncertainties

Which particle counts as a fundamental particle?

Fundamental particles

On a planet, a projectile launched vertically upward takes $12.5\,\text{ s}$ to come back to where it started. Its greatest height is $170\,\text{ m}$. There is no atmosphere on the planet. Determine the acceleration of free fall on this planet?

Equations of motion

A displacement-time graph for a toy car is displayed. Which graph shows how the car’s velocity $v$ changes with time?

Equations of motion

A driver brings a car to rest in time $t$ by steadily increasing the overall braking force acting on it. The graph shows the resultant force on the car. Which graph shows how the car’s speed changes over this period?

Non-uniform motion

The graph illustrates how a quantity $y$ changes with a quantity $x$ for an object falling through air at constant (terminal) velocity in a uniform gravitational field. Which quantities might $x$ and $y$ be?

Equations of motion

A ball with mass $2.0\,\text{kg}$ is moving horizontally at a speed of $4.0\,\text{m s}^{-1}$. It hits a wall and then rebounds in the opposite direction at a speed of $2.8\,\text{m s}^{-1}$. The collision lasts for $150\,\text{ms}$. What is the average force exerted on the wall?

Momentum and Newton's laws of motion