May/June 2014

Which pair of units includes one derived unit and one SI base unit?

SI units

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

Momentum and Newton's laws of motion

The diagrams illustrate two different ways of suspending the same picture. In each case, a string is fixed to the same points on the picture and arranged symmetrically over a nail in a wall. The forces shown are the ones acting on the nail. In diagram 1, the string loop is shorter than it is in diagram 2. Which statement about the magnitude of the forces is correct?

Equilibrium of forces

A man is supporting a $100\,\text{N}$ load motionless in his hand. The total weight of the forearm and hand is $20\,\text{N}$. The forearm remains horizontal, as shown. What vertical force $F$ is required in the biceps?

Turning effects of forces

A spindle is fixed at one end to the midpoint of a lever with length $1.20\,\text{m}$ and at the other end to the midpoint of a disc with radius $0.20\,\text{m}$. A string is wound around the disc, goes over a pulley and is connected to a $900\,\text{N}$ weight. What is the smallest force $F$, applied at each end of the lever, that could raise the weight?

Turning effects of forces

What is the mean power output of a laser that delivers $0.20\,\text{J}$ of energy in $10\,\text{ns}$?

Potential difference and power

A weight $W$ is suspended from a trolley travelling along a rail. While the trolley moves horizontally by a distance $p$, it at the same time lifts the weight through a height $q$. Hence, the weight is displaced a distance $r$ from X to Y. It begins and ends at rest. What amount of work is done on the weight in this process?

Gravitational potential energy and kinetic energy

A car's engine applies a force of $600\,\text{N}$ while the car is moved $1.0\,\text{km}$ in $150\,\text{s}$. What is the average output power of the engine?

Energy conservation

Which of the following statements about boiling and evaporation is correct?

Energy conservation

At a single temperature, approximately $0.01^{\circ}\text{C}$, water, water vapour and ice are able to exist together in equilibrium. Which statement about the molecules’ properties at this temperature is correct?

Physical quantities

A crystalline solid is heated at a steady rate, and the graph below shows how the temperature changes with time. Which statement about the particles in the material is correct?

Energy conservation

What value is equal to 2000 microvolts?

SI units

Stress-strain graphs for three different materials are shown; they are not plotted to the same scale. These materials are copper, rubber and glass. Which material corresponds to each graph?

Stress and strain

The graph shown is a load-extension graph for a wire that is being elastically deformed. What amount of work is done on the wire in order to increase the extension from $10\,\text{mm}$ to $20\,\text{mm}$?

Elastic and plastic behaviour

Which one of the following statements about longitudinal waves is correct?

Transverse and longitudinal waves

The order of magnitude for the frequency of the ultraviolet waves with the longest wavelength can be written as $10^x\,\text{Hz}$. What is the value of $x$?

Electromagnetic spectrum

The wave speed $v$ in deep water is related by $v^2 = \dfrac{g\lambda}{2\pi}$ in which $\lambda$ represents the wavelength of the waves and $g$ denotes the acceleration of free fall. A student records the wavelength $\lambda$ and the frequency $f$ for several of these waves. Which graph ought he to plot so that the result is a straight line passing through the origin?

Progressive waves

A stationary wave is formed on a stretched string between points P and T. Which statement about the wave is correct?

Stationary waves

A parallel beam of white light is directed through a diffraction grating. Orange light with wavelength $600\,\text{nm}$ in the fourth-order diffraction maximum overlaps with blue light in the fifth-order diffraction maximum. What is the wavelength of the blue light?

The diffraction grating

The essential idea behind note formation in a horn is to establish a stationary wave within an air column. For every note the horn makes, a node appears at the mouthpiece and an antinode appears at the bell. The frequency of the lowest note is $75\,\text{Hz}$. What are the frequencies of the following two higher notes for this air column?

Stationary waves

A horizontal beam of electrons is directed between two horizontal parallel plates that are $2.0\,\text{cm}$ apart. The top plate is at an electrical potential of $+4.0\,\text{V}$, and the bottom plate is at an electrical potential of $-4.0\,\text{V}$. What is the force on each electron while it is between the plates?

Potential difference and power

In the diagram, the two points $P$ and $Q$ are positioned on a circle of radius $r$ so that they are $90^\circ$ apart. 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

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

Physical quantities

Two electrically conducting cylinders $X$ and $Y$ are made from the same material. Their dimensions are shown. The resistance measured across the ends of each cylinder is taken. What is the ratio $\frac{\text{resistance of } X}{\text{resistance of } Y}$?

Resistance and resistivity

A battery, having a constant internal resistance, is connected to a resistor with resistance $250\,\Omega$, as shown. The current in the resistor is $40\,\text{mA}$ for $60\,\text{s}$. Over this interval, $6.0\,\text{J}$ of energy is dissipated in the internal resistance. What are the energy delivered to the external resistor in the $60\,\text{s}$ and the e.m.f. of the battery?

Potential difference and power

Which symbol represents a component whose resistance is intended to vary with temperature?

Practical circuits

In the circuit shown below, a voltmeter with resistance $R_V$ and an ammeter with resistance $R_A$ are connected to determine the resistance $R$ of the fixed resistor. Which condition is required if an accurate value of $R$ is to be found?

Practical circuits

In the circuit diagram shown, every resistor is identical, and the resistance of each ammeter is negligible. Ammeter $A_1$ shows a reading of $0.6\,\text{A}$. What readings do the other ammeters show?

Kirchhoff's laws

A component in a circuit has a potential difference of $2.0\,\text{V}$ across it. How many electrons must pass through the component for $4.8\,\text{J}$ of energy to be transferred to it?

Potential difference and power

What is the combined resistance between points $P$ and $Q$ in this resistor network?

Kirchhoff's laws

Alpha, beta and gamma radiations differ in the depth to which they can penetrate matter and also in their charges. Which row gives the best summary of the penetration and charge of each type of radiation?

Atoms, nuclei and radiation

In 2002, an isotope of iron, $^{45}_{26}\text{Fe}$, was observed to undergo two-proton radioactive decay. What product could result?

Atoms, nuclei and radiation

The ion $\text{U}^{++}$ represents a uranium atom that has been doubly ionised. This uranium atom has a nucleon number of $235$ and a proton number of $92$. Using a simple model of the atom, how many particles are present in this ionised atom?

Atoms, nuclei and radiation

A practical investigation is done to determine the resistance of a wire. The current in the wire is $(1.0 \pm 0.2)\,\text{A}$ and the potential difference across the wire is $(8.0 \pm 0.4)\,\text{V}$. Calculate the resistance of the wire and its uncertainty.

Resistance and resistivity

The grid displays several nuclides arranged by the number of protons and the number of neutrons in each one. A nucleus of the nuclide $^{8}_{3}\text{Li}$ decays by releasing a $\beta$-particle. What is the nuclide formed?

Atoms, nuclei and radiation

The Young modulus of a wire’s material is to be determined. The Young modulus $E$ is given by the equation $E = \dfrac{4Fl}{\pi d^2 x}$. A known force is used to stretch the wire, and these measurements are recorded. Which measurement contributes the greatest uncertainty to the calculated value of the Young modulus?

Errors and uncertainties

A tennis ball is projected horizontally through the air from the top of a tall building. If the effect of air resistance is not negligible, what happens to the ball’s horizontal and vertical components of velocity?

Non-uniform motion

An object is projected vertically upwards on the Moon with a velocity of $5.2\,\text{m s}^{-1}$. The Moon’s acceleration due to gravity is $1.62\,\text{m s}^{-2}$. What time does the object take to return to the point from which it was launched?

Equations of motion

The graph illustrates the way in which the acceleration of an object moving along a straight line changes with time. At the start, the object is at rest. Which graph shows how the velocity of the object changes with time over the same time interval?

Equations of motion

A body with mass $4.0\,\text{kg}$ and speed $3.0\,\text{m s}^{-1}$ collides with a stationary object in an inelastic collision. Which statement is correct?

Linear momentum and its conservation

The equation $P = k \rho A v^n$ gives the maximum theoretical power $P$ of a wind turbine, where $\rho$ represents the density of air, $A$ denotes 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 $n$?

Gravitational potential energy and kinetic energy

A tractor with mass $1000\,\text{kg}$ is attached to a trailer of mass $1000\,\text{kg}$ by a tow-bar. The overall resistance to motion is constant and equal to $4000\,\text{N}$. A quarter of this resistance acts on the trailer. If the tractor and trailer are travelling over horizontal ground at a steady speed of $6\,\text{m s}^{-1}$, what force does the tow-bar exert on the tractor?

Equilibrium of forces

The graph illustrates how the speed of a raindrop falling vertically through air changes with time. Which statement is correct?

Non-uniform motion

A very small oil droplet of mass $6.9 \times 10^{-13}\,\text{kg}$ is stationary in an electric field of electric field strength $2.1 \times 10^{7}\,\text{N C}^{-1}$, as illustrated. The droplet’s weight is exactly counterbalanced by the electric force acting on it. Determine the charge on the droplet.

Electric current

The diagram illustrates four forces acting on a circular object. Which of the following states the resultant force and resultant torque on the object?

Turning effects of forces

A mass at point X within a uniform gravitational field is acted on by a gravitational force of $0.200\,\text{N}$. Its gravitational potential energy is $1.00\,\text{J}$. The mass is then relocated to point Y. What is the gravitational potential energy now?

Gravitational potential energy and kinetic energy

A small mass is set down at point P on the inner surface of a smooth hemisphere, and it is then released from rest. When it arrives at the lowest point T, its speed is $4.0\,\text{m s}^{-1}$. The diagram, which is not to scale, shows the mass’s speed at other points Q, R and S while it slides down. Air resistance is negligible. From P to T, the mass loses potential energy $E$. At which point has the mass lost potential energy $\frac{E}{4}$?

Gravitational potential energy and kinetic energy

An escalator measures $60\,\text{m}$ in length and raises passengers by a vertical distance of $30\,\text{m}$, as illustrated. When there are no passengers on it, the power needed to drive the escalator against friction is $2.0\,\text{kW}$. The escalator carries passengers with an average mass of $60\,\text{kg}$, while the power needed to overcome friction stays constant. What power is needed to drive the escalator when it is carrying $20$ passengers and moving upwards at $0.75\,\text{m s}^{-1}$?

Gravitational potential energy and kinetic energy

If the Universe were such that, as temperature rose, the speed of the molecules in a substance increased, but at any given temperature every molecule in that substance had the same speed, which process would not take place?

Density and pressure

The density of liquid Q is double that of liquid R. When the depth in liquid R is $x$, the pressure caused by the liquid is $4\,\text{kPa}$. At what depth in liquid Q does the pressure caused by the liquid become $7\,\text{kPa}$?

Density and pressure

A metal sample is pulled by a force that rises to a peak value and then falls again to zero. The force-extension graph for the sample is shown below. As the sample shortens, it retraces the same force-extension curve that it followed while being stretched. What happens to the metal between X and Y?

Elastic and plastic behaviour

What SI base units are used to express resistance?

Resistance and resistivity

The graph illustrates how the length of a spring changes when a larger load is applied and it is stretched. What is the spring constant?

Stress and strain

A composite rod is produced by joining, end to end, a glass-reinforced plastic rod and a nylon rod, as shown. The rods each have the same cross-sectional area, and every rod is $1.00\,\text{m}$ long. The Young modulus $E_p$ of the plastic is $40\,\text{GPa}$, and the Young modulus $E_n$ of the nylon is $2.0\,\text{GPa}$. The composite rod breaks once its total extension reaches $3.0\,\text{mm}$. What is the maximum tensile stress that can be applied to the composite rod before it breaks?

Stress and strain

To two significant figures, what are the period, frequency and amplitude of the wave shown on the graph?

Progressive waves

A sound wave is made up of a sequence of travelling pressure changes away from the usual, steady air pressure. The graph illustrates these pressure changes for two waves at a single moment in time. Wave 1 has an intensity of $1.6 \times 10^{-6}\ \text{W m}^{-2}$. What intensity does wave 2 have?

Progressive waves

The diagram depicts a vertical section through a water wave travelling from left to right. At which point is the water moving upwards at its greatest speed?

Progressive waves

The principle of superposition states that a particular quantity is combined when two or more waves meet at a point. What is this quantity?

Interference

Light is sent through a diffraction grating with $1000$ lines per cm, and the same wavelength of light is also sent through two narrow slits separated by $0.5\ \text{mm}$. In each case, the screen shows intensity maxima and minima. Which statement about how far apart the maxima are on the screen and how sharp the maxima are is correct?

The diffraction grating

The diagram illustrates an arrangement that has been assembled to show two-source interference. Microwaves with wavelength $\lambda$ travel through two slits $S_1$ and $S_2$. The detector is displaced away from point O in the direction shown by the arrow. The signal received falls until the detector arrives at point X, then rises again once the detector moves past X. Which equation gives the position of X correctly?

Interference

At the vertices of an equilateral triangle, there are two positive charges and one negative charge, each with the same magnitude. Which diagram best shows the electric field around the charges?

Scalars and vectors

Two horizontal metal plates carrying opposite charges are positioned in a vacuum. A particle with positive charge begins at rest and travels from one plate to the other plate, as shown. Which graph shows how the kinetic energy $E_K$ of the particle changes with the distance $x$ travelled from the positive plate?

Potential difference and power

A cathode-ray oscilloscope (c.r.o.) is connected to an alternating voltage, and the screen shows the trace below. The oscilloscope time-base setting is $0.5\,\text{ms cm}^{-1}$ and the Y-plate sensitivity is $2\,\text{V cm}^{-1}$. Which statement about the alternating voltage is correct?

Practical circuits

A battery with electromotive force (e.m.f.) $V$ and negligible internal resistance is connected to a $1\,\text{k}\Omega$ resistor, as shown. A student tries to measure the potential difference (p.d.) between points P and Q using two voltmeters, one after the other. The first voltmeter has a resistance of $1\,\text{k}\Omega$ and the second voltmeter has a resistance of $1\,\text{M}\Omega$. What are the readings of the voltmeters?

Practical circuits

A copper wire is to be substituted with an aluminium alloy wire that has the same length and the same resistance. The resistivity of copper is half that of the alloy. What is the ratio $\frac{\text{diameter of alloy wire}}{\text{diameter of copper wire}}$ ?

Resistance and resistivity

The diagram shows an electric pump for a garden fountain that is linked to a $230\,\text{V}$ mains electrical supply by an $18\,\text{m}$ cable. The pump is considered to be performing acceptably when the potential difference (p.d.) across it is at least $218\,\text{V}$. At that point, the current through it is $0.83\,\text{A}$. What is the greatest resistance per metre of each of the two wires in the cable if the pump is to perform acceptably?

Resistance and resistivity

For cell X, the e.m.f. is $2.0\,\text{V}$ and the internal resistance is $2.0\,\Omega$. For cell Y, the e.m.f. is $1.6\,\text{V}$ and the internal resistance is $1.2\,\Omega$. The two cells are connected to a resistor of resistance $0.8\,\Omega$, as illustrated. What is the current in cell X?

Kirchhoff's laws

In the circuit diagram, a light-dependent resistor (LDR) is connected to two resistors $R_1$ and $R_2$. The potential difference (p.d.) across $R_1$ is $V_1$, while the p.d. across $R_2$ is $V_2$. The current flowing in the circuit is $I$. Which statement about this circuit is correct?

Potential dividers

A power supply is being compared with a solar cell by means of the potentiometer circuit shown. The e.m.f. of the solar cell is obtained with the potentiometer. The potentiometer wire $PQ$ has a length of $100.0\,\text{cm}$ and a resistance of $5.00\,\Omega$. The power supply has an e.m.f. of $2.000\,\text{V}$, while the solar cell has an e.m.f. of $5.00\,\text{mV}$. Which resistance $R$ should be used so that the galvanometer gives a zero reading when $PS = 40.0\,\text{cm}$?

Practical circuits

In the circuit diagram, every resistor has the same value. Voltmeter $V_1$ reads $8.0\,\text{V}$ and voltmeter $V_2$ reads $1.0\,\text{V}$. What readings do the other voltmeters show?

Potential dividers

The diagram illustrates a light-dependent resistor (LDR) and a thermistor arranged as a potential divider. Under which conditions will the potential difference across the thermistor be at its maximum?

Potential dividers

A nucleus $X$ undergoes decay to become a nucleus $Y$ by first emitting an alpha particle and then two beta particles. Which statement concerning this nuclear decay is correct?

Atoms, nuclei and radiation

A slow neutron strikes a uranium-235 nucleus. The nuclear reaction is shown by this equation: $^{235}_{92}\text{U} + ^{1}_{0}\text{n} \rightarrow ^{154}_{60}\text{Nd} + ^{80}_{32}\text{Ge} + x$ In this expression, $x$ stands for one or more particles. What is $x$?

Atoms, nuclei and radiation

A value $y$ is to be found using the equation below. $y = \frac{px}{q^2}$ The percentage uncertainties for $p$, $x$ and $q$ are given. What is the percentage uncertainty in $y$?

Errors and uncertainties

Scientists produced the first artificial radioactive substance by firing $\alpha$-particles at aluminium, $^{27}_{13}\text{Al}$. The result was an unstable isotope of phosphorus, $^{30}_{15}\text{P}$. What was produced as the by-product of this reaction?

Atoms, nuclei and radiation

A thermometer may be read with an accuracy of $\pm 0.5^{\circ}\text{C}$. It is used to measure a temperature increase from $40^{\circ}\text{C}$ to $100^{\circ}\text{C}$. What is the percentage uncertainty in the measurement of the temperature increase?

Errors and uncertainties

A radio-controlled toy car moves in a straight line over a period of $15\,\text{s}$. The graph shows how the car’s velocity $v$ changes with time $t$. What is the toy car’s average velocity for the journey represented by the graph?

Non-uniform motion

Two train carriages, each with a mass of $5000\,\text{kg}$, move towards one another on a level track. One is moving at $2.00\,\text{m s}^{-1}$ and the other at $1.00\,\text{m s}^{-1}$, as shown. They collide and stick together. What is the kinetic energy lost during the collision?

Linear momentum and its conservation

When a resultant force acts on a body, it accelerates. What is the resultant force equal to?

Momentum and Newton's laws of motion

A ship with mass $8.4 \times 10^7\,\text{kg}$ is moving towards a harbour at a speed of $16.4\,\text{m s}^{-1}$. If reverse thrust provides a steady total stopping force of $920\,000\,\text{N}$, Calculate the time taken to bring it to rest.

Momentum and Newton's laws of motion

Which physical quantity may be expressed in electronvolts (eV)?

Energy conservation

A tennis ball is released above a table and rebounds after striking it. The table applies a force $F$ to the ball. Which graph most accurately shows how the force $F$ varies with time $t$ during the period when the ball is touching the table?

Linear momentum and its conservation

For a time interval of $2.0\,\text{s}$, a body is acted on by a resultant force of $10\,\text{N}$. Which graph might represent how the momentum $p$ of the body changes with time $t$?

Momentum and Newton's laws of motion

A body at rest breaks apart into two fragments with masses $m$ and $2m$. The fragments acquire kinetic energies $X$ and $Y$, in that order. What is the value of the ratio $\frac{X}{Y}$?

Linear momentum and its conservation

What condition must an object satisfy to be in equilibrium?

Equilibrium of forces

A uniform solid cuboid made of concrete, with dimensions $0.50\,\text{m} \times 1.20\,\text{m} \times 0.40\,\text{m}$ and weight $4000\,\text{N}$, is at rest on a level surface with the $1.20\,\text{m}$ edge upright, as illustrated in diagram 1. Calculate the least energy needed to rotate the cuboid through $90^{\circ}$ into the arrangement shown in diagram 2, where the $0.50\,\text{m}$ edge is upright.

Gravitational potential energy and kinetic energy

A uniform beam is pivoted at $P$ as illustrated. Weights of $10\,\text{N}$ and $20\,\text{N}$ are fixed to its two ends. The beam is labelled at $0.1\,\text{m}$ intervals. The beam itself weighs $100\,\text{N}$. At what point must an additional weight of $20\,\text{N}$ be attached so that the beam is in equilibrium?

Turning effects of forces

An electric motor has an input power $P_{in}$, useful output power $P_{out}$ and efficiency $\eta$. What is the power lost in the motor?

Energy conservation

A shot-put champion speeds up a $7.0\,\text{kg}$ metal ball along a straight path. Starting from rest, the ball reaches a speed of $12\,\text{m s}^{-1}$ over a distance of $1.2\,\text{m}$. What is the average resultant force acting on the metal ball?

Equations of motion

A ball falls onto a horizontal surface and rebounds elastically. What occurs to the ball’s kinetic energy over the very brief interval while it is touching the surface?

Elastic and plastic behaviour

When water in a pond freezes, it changes state from liquid to solid. As this happens, its volume changes and energy is transferred to or from the surroundings. Which row is correct?

Energy conservation

The unit of specific heat capacity is $\text{J kg}^{-1}\text{K}^{-1}$. How is this expressed using SI base units?

SI units

Which process does not need energy to be provided?

Energy conservation

The graph illustrates how the speeds of the molecules in a gas are distributed at a given temperature. Which statement is correct?

Atoms, nuclei and radiation

The Mariana Trench in the Pacific Ocean is roughly $10\,\text{km}$ deep. If sea water is taken to be incompressible and to have a density of about $1020\,\text{kg m}^{-3}$, what is the approximate pressure at that depth?

Density and pressure

For an elastic material with Young modulus $E$, a tensile stress $S$ is applied. Hooke’s Law holds. What expression gives the elastic energy stored per unit volume of the material?

Stress and strain

Each of the following cylindrical specimens — steel, glass and rubber — is acted on by a tensile force $F$ that is increased steadily. The extensions $e$ are recorded, and the graphs are drawn as shown below. Which row gives the correct matching between the graphs and the materials?

Elastic and plastic behaviour

A cathode-ray oscilloscope (c.r.o.) shows a waveform that represents a sound wave. To find the frequency of the sound wave, which section of the displayed waveform should be measured, and which c.r.o. setting has to be known?

Progressive waves

What approximate frequency range does infra-red radiation have?

Electromagnetic spectrum

A small source produces spherical waves. The wave intensity $I$ at a point $P$, which is a distance $r$ from the source, varies inversely as $r^2$. What relationship exists between the wave amplitude $a$ and the distance $r$?

Progressive waves

A student tries to demonstrate light interference using two matching green LEDs. Which statement explains why this experiment will not work?

Interference

A stationary wave forms on a stretched string, as illustrated. Which statement about the points on the string is correct?

Stationary waves

What is the vertical part of this displacement vector?

Scalars and vectors

Monochromatic light falls on a diffraction grating, and a diffraction pattern is seen. Which row in the table shows the effect of changing the grating to one with a greater number of lines per metre?

The diffraction grating

An electron moves into a region of space containing a uniform electric field $E$, as illustrated. At the start, the electron travels parallel to the electric field and in the same direction as it. What path does the electron then follow, and how does its speed change?

Equations of motion

Two parallel plates X and Y are spaced a distance $d$ apart in a vacuum. A potential difference exists between the plates, creating a uniform electric field. A charge $-q$ starts from rest at the surface of plate X and moves towards plate Y. By the time the charge arrives at plate Y, its kinetic energy is $K$. Which expression gives the electric field strength between the plates?

Potential difference and power

Wires P and Q are made from the same material and have the same length. They are connected in parallel to one voltage supply. The diameter of wire P is $2\,\text{mm}$ and the diameter of wire Q is $1\,\text{mm}$. Determine the ratio $\dfrac{\text{current in P}}{\text{current in Q}}$?

Resistance and resistivity

A cell has an electromotive force (e.m.f.) of $6\,\text{V}$ and internal resistance $R$. An external resistor, which also has resistance $R$, is connected across the cell, as illustrated. Power $P$ is dissipated in the external resistor. The cell is then replaced with another cell that has an e.m.f. of $6\,\text{V}$ and negligible internal resistance. What is the new power dissipated in the external resistor?

Potential difference and power

The diagram depicts a low-voltage circuit used to heat the water in a fish tank. The heater has a resistance of $3.0\,\Omega$. The power supply has an e.m.f. of $12\,\text{V}$ and an internal resistance of $1.0\,\Omega$. At what rate is energy transferred to the heater?

Potential difference and power

The diagrams represent the same cell, ammeter, potentiometer and fixed resistor arranged in different configurations. The distance $d$ between the sliding contact and one specified end of the potentiometer is changed. The current measured is then graphed against distance $d$. For which two circuits will the graphs be the same?

Practical circuits

What current flows through the $40\,\Omega$ resistor in the circuit shown?

Kirchhoff's laws

A battery with negligible internal resistance is connected to a resistor network, an ammeter and a switch $S$, as illustrated. With $S$ open, the ammeter reading is $250\,\text{mA}$. With $S$ closed, what change occurs in the ammeter reading?

Practical circuits

One thorium isotope has nucleon number $232$ and proton number $90$. It decays to produce a different thorium isotope with nucleon number $228$. Determine how many alpha particles and beta particles are emitted by the thorium nucleus during this decay.

Atoms, nuclei and radiation

The resistance of a lamp is found using the value of the potential difference (p.d.) across it and the value of the current flowing through it. Which statement gives the correct way to combine the uncertainties in the p.d. and in the current?

Errors and uncertainties

The four nuclei are shown below. $^{28}_{14}E\quad ^{25}_{15}G\quad ^{25}_{12}M\quad ^{24}_{13}Q$ Which of the following statements about these nuclei is correct?

Atoms, nuclei and radiation

The screen of a cathode-ray oscilloscope shows the output from an electronic circuit. The time-base is adjusted to $5.0\,\text{ns}$ per division and the Y-gain to $10\,\text{V}$ per division. What is the frequency of the signal?

Progressive waves

A digital caliper is being used to measure the $28.50\,\text{mm}$ width of a plastic ruler. The digital caliper shows readings to the nearest $0.01\,\text{mm}$. How should this reading be recorded correctly?

Errors and uncertainties

An experiment is carried out to determine the acceleration of free fall $g$. A body drops between two fixed points. The four readings shown below are recorded. Which reading is not needed for the calculation of $g$?

Equations of motion

In a cathode-ray tube, an electron moves with uniform acceleration in a straight line, increasing its speed from $4 \times 10^{3}\,\text{m s}^{-1}$ to $2 \times 10^{7}\,\text{m s}^{-1}$ across a distance of $10\,\text{mm}$. What is the electron's acceleration?

Equations of motion

The graph illustrates how the speed $v$ of a sprinter varies with time $t$ in a $100\,\text{m}$ race. What is the best estimate of the sprinter’s greatest acceleration?

Non-uniform motion