May/June 2013

Which pair of quantities includes one vector quantity and one scalar quantity?

Scalars and vectors

Which one of the following correctly states the principle of conservation of momentum?

Linear momentum and its conservation

A $2.0\,\text{kg}$ mass, moving at $3.0\,\text{m s}^{-1}$ across a frictionless surface, collides head-on with a $1.0\,\text{kg}$ mass that is initially at rest. The two masses join together after the impact. What kinetic energy is lost in the collision?

Linear momentum and its conservation

A car with mass $750\,\text{kg}$ experiences a horizontal driving force of $2.0\,\text{kN}$. It moves with a forward horizontal acceleration of $2.0\,\text{m s}^{-2}$. What is the horizontal resistive force?

Momentum and Newton's laws of motion

A tiny water droplet with mass $3.0\,\mu\text{g}$ has a charge of $-6.0 \times 10^{-11}\,\text{C}$. It is placed in the Earth’s gravitational field between two horizontal metal plates. The upper plate is at a potential of $+500\,\text{V}$, while the lower plate is at a potential of $-500\,\text{V}$. The plates are $2.0\,\text{mm}$ apart. What is the droplet’s motion?

Potential difference and power

A horizontal bar rests on a pivot placed at its centre of gravity. A fixed load is fastened to one end of the bar. To maintain equilibrium, a force $F$ is exerted at a distance $x$ from the pivot. How does $F$ depend on $x$?

Turning effects of forces

The diagram shows a sphere submerged in water. $P$, $Q$, $R$ and $S$ are forces on the sphere caused by the pressure of the water. 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 these forces is correct?

Density and pressure

A cable keeps a hinged trapdoor closed while it is in the horizontal position. The trapdoor is acted on by three forces: the weight $W$ of the door, the tension $T$ in the cable, and the force $H$ at the hinge. Which list arranges these three forces in order of increasing magnitude?

Equilibrium of forces

A solid rubber ball with a diameter of $8.0\,\text{cm}$ is let go from rest with the top of the ball $80\,\text{cm}$ above a horizontal surface. It moves straight down and then rebounds so that the greatest height attained by the top of the ball is $45\,\text{cm}$, as shown. If the kinetic energy of the ball is $0.75\,\text{J}$ immediately before it hits the surface, what is its kinetic energy immediately after it has left the surface?

Gravitational potential energy and kinetic energy

The blades of a wind turbine sweep out an area of $2000\,\text{m}^2$. It changes the power in the wind into electrical power with an efficiency of $50\%$. How much electrical power is produced when the wind speed is $10\,\text{m s}^{-1}$? (The density of air is $1.3\,\text{kg m}^{-3}$.)

Energy conservation

The diagram depicts a wheel with a circumference of $0.30\,\text{m}$. One end of a rope is attached to a force meter. The rope runs over the wheel and carries a load of $100\,\text{N}$ hanging freely. The wheel is powered by an electric motor and rotates steadily at $50\,\text{revs s}^{-1}$. At this rotational speed, the force meter gives a reading of $20\,\text{N}$. What is the motor's output power?

Energy conservation

A material has a property $Q$ that is used to describe how sound waves behave in the material. $Q$ is given by the pressure $P$ of the sound wave divided by the wave speed $v$ and the surface area $A$ of the material through which the wave passes: $Q = \frac{P}{vA}.$ What are the SI base units of $Q$?

SI units

Which row gives the correct characteristics of the process of evaporation?

Energy conservation

A bore-hole with a depth of $2000\,\text{m}$ contains oil and water, as illustrated. The pressure caused by the liquids at the base of the bore-hole is $17.5\,\text{MPa}$. The density of the oil is $830\,\text{kg m}^{-3}$ and the density of the water is $1000\,\text{kg m}^{-3}$. What is the depth $x$ of the oil?

Density and pressure

The stress-strain graphs for four different materials are displayed below. Which diagram represents the stress-strain graph of a ductile metal?

Elastic and plastic behaviour

Several identical springs, all with the same spring constant, are connected in four different arrangements. A different load is placed on each arrangement. Which arrangement produces the greatest extension?

Elastic and plastic behaviour

A light wave with amplitude $A$ falls normally on a surface of area $S$. The power per unit area arriving at the surface is $P$. The amplitude of the light wave is then raised to $2A$. The light is afterwards focussed onto a smaller area $\frac{1}{3}S$. What is the power per unit area on this smaller area?

Progressive waves

A wave travels at $340\,\text{m s}^{-1}$ and has a period of $0.28\,\text{ms}$. What is the wavelength of the wave?

Progressive waves

Which row of the table gives the variation in wave characteristics as you move from infra-red to ultraviolet in the electromagnetic spectrum?

Electromagnetic spectrum

Light with wavelength $600\,\text{nm}$ falls on a pair of slits, producing fringes that are spaced $4.0\,\text{mm}$ apart on a screen. What is the fringe spacing if the wavelength is changed to $400\,\text{nm}$ and the slit separation is doubled?

Interference

The speed of a transverse wave on a stretched string may be altered by changing the tension in the string. A stationary wave pattern is produced on a stretched string by an oscillator operating at a frequency of $650\,\text{Hz}$. What change must be made to the wave so that the same stationary wave pattern is kept when the applied frequency is raised to $750\,\text{Hz}$?

Stationary waves

Noise reduction headphones create their own sound waves to cancel external sound waves. Inside the headphones, a microphone detects waves of one frequency. A loudspeaker in the headphones then emits a wave with that same frequency but at a different phase. What phase difference is there between the external sound wave and the wave produced by the loudspeaker in the headphones?

Interference

A cannon launches a cannonball with initial speed $v$ at an angle $\alpha$ above the horizontal. Which equation gives the maximum height $H$ attained?

Equations of motion

An electron beam enters an electric field and is turned away by it. Diagram 1 shows an electric field lying in the plane of the paper. Diagram 2 shows an electric field acting at right angles to the plane of the paper. The lines A, B, C and D show possible routes for the electron beam. Every route lies in the plane of the paper. Which line most accurately shows the electrons’ path within the field?

Equations of motion

As shown, two parallel plates carry opposite charges. An electron is let go from rest at the surface of the negatively charged plate, and it moves from that plate towards the positively charged plate. Which graph indicates how the force $F$ acting on the electron changes with its distance $x$ from the negative plate?

Potential difference and power

A $13\,\Omega$ resistor is connected in series to a power supply whose electromotive force (e.m.f.) is $12\,\text{V}$ and whose internal resistance is $2.0\,\Omega$. What power is dissipated in the $13\,\Omega$ resistor?

Potential difference and power

When a battery is connected to a resistor, the battery slowly heats up. This makes the battery's internal resistance rise while its e.m.f. remains the same. As the internal resistance of the battery rises, what happens, if anything, to the terminal potential difference and the output power?

Potential difference and power

Which two quantities are linked to the conservation principles behind Kirchhoff’s first and second laws?

Kirchhoff's laws

The circuit below is connected to a $3\text{ V}$ battery. Every resistance is $1\text{ k}\Omega$. What reading will the voltmeter show?

Practical circuits

The diagram depicts a circuit that has been connected wrongly. The ammeter has a resistance of $0.1\Omega$ and the voltmeter has a resistance of $1\text{ M}\Omega$. Which statement is true?

Practical circuits

A $12\text{ V}$ battery is connected in series with an ammeter, a $2\Omega$ fixed resistor and a $0$-$10\Omega$ variable resistor. A voltmeter with high resistance is placed across the variable resistor. The variable resistor is adjusted from zero up to its highest resistance. Which graph shows the way the potential difference (p.d.) reading on the voltmeter changes as the current reading on the ammeter changes?

Potential dividers

A nickel nucleus $^{59}_{28}\text{Ni}$ may be altered by a process known as K-capture. In this process, the nucleus takes in an orbital electron. If no other process occurs, which nucleus is formed?

Atoms, nuclei and radiation

At one time it was believed that an atom’s mass is distributed evenly throughout the atom’s volume. When $\alpha$-particles are aimed at a sheet of gold foil, the observations caused scientists to conclude instead that almost all the mass of the gold atom is concentrated at a single point within the atom. Which effect could occur only if almost all the mass of the gold atom is concentrated at a point?

Atoms, nuclei and radiation

A wave has a frequency of $5\,\text{GHz}$. Calculate the period of the wave.

Progressive waves

Which two nuclei are isotopes of each other?

Atoms, nuclei and radiation

In an experiment used to find the acceleration of free fall $g$, the period of oscillation $T$ and the length $l$ of a simple pendulum were recorded. The estimated uncertainty in the measurement of $l$ is $4\%$, while the estimated uncertainty in the measurement of $T$ is $1\%$. The value of $g$ is found from $g = \frac{4\pi^2 l}{T^2}$. What uncertainty is there in the calculated value of $g$?

Errors and uncertainties

The Y-input terminals on a cathode-ray oscilloscope (c.r.o.) are connected to a supply with amplitude $5.0\,\text{V}$ and frequency $50\,\text{Hz}$. The time-base is adjusted to $10\,\text{ms}$ per division, and the Y-gain is set to $5.0\,\text{V}$ per division. Which trace is produced?

Practical circuits

A body is let go from rest and drops vertically through air of constant density. Which statement about the body's motion is correct?

Non-uniform motion

A goods train travels through a station at a constant speed of $10\,\text{m s}^{-1}$. An express train is stationary at the station. At the instant the goods train passes, the express train starts from the station with a uniform acceleration of $0.5\,\text{m s}^{-2}$. The two trains travel in the same direction along straight, parallel tracks. After how much time does the express train overtake the goods train?

Equations of motion

A car is at rest at traffic lights. When the lights turn green, the driver depresses the accelerator sharply. The resulting horizontal force on the car changes with time as shown. Which graph shows how the car’s speed varies with time?

Non-uniform motion

Which pair contains one vector quantity and one scalar quantity?

Scalars and vectors

Two bodies moving along a straight line undergo a perfectly elastic collision. Which of the following statements must be true?

Linear momentum and its conservation

A submarine is balanced while completely underwater. What is the reason for the upthrust acting on the submarine?

Density and pressure

A vehicle is stationary on an incline. It is taken to have three forces acting on it so that it remains in equilibrium. These are its weight $W$, a normal reaction force $R$ and a frictional force $F$. Which triangle of forces is correct?

Equilibrium of forces

All external forces acting on a body balance each other out. Which statement must be correct?

Equilibrium of forces

A uniform beam of mass $1.4\,\text{kg}$ is supported at the pivot $P$ as shown. 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 $6.0\,\text{kg}$ hang from the beam at distances of $0.35\,\text{m}$ and $0.15\,\text{m}$ from the pivot, as shown. What torque is needed to be applied to keep the beam in equilibrium?

Turning effects of forces

A ball is projected vertically upward. If air resistance is ignored, which statement is correct?

Equations of motion

A bow with a mass of $400\,\text{g}$ propels an arrow of mass $120\,\text{g}$ straight upwards. Immediately before release, the bow stores $80\,\text{J}$ of potential energy. The efficiency of the system is $28\%$. What height does the arrow reach if air resistance is ignored?

Gravitational potential energy and kinetic energy

An engine is pulling a train along a mountain railway track that is inclined at an angle of $30^\circ$ to the horizontal. The train is transporting $200$ passengers, each with an average mass of $70\,\text{kg}$, and it is moving at $6.0\,\text{m s}^{-1}$. The mass of the train itself is $80\,000\,\text{kg}$. Of the power supplied by the engine, $40\%$ is used to lift the train and its passengers. Calculate the power of the engine?

Gravitational potential energy and kinetic energy

A gas is trapped in a cylinder that has a frictionless piston fitted to it. At the start, the gas occupies a volume $V_1$ and is in equilibrium with an outside pressure $p$. The gas is then heated gradually so that it expands, driving the piston backwards until the gas volume becomes $V_2$. How much work is done by the gas in this expansion?

Energy conservation

The diagram depicts an ice cube floating in water. Both the ice cube and the water are at $0^\circ\text{C}$. Which statement gives the correct comparison between the molecular properties of the ice and the water?

Density and pressure

The SI base-unit form of resistivity is given by $\text{kg } x^3 y^{-2} z^{-3}$. What are $x$, $y$ and $z$?

Resistance and resistivity

Two bulbs X and Y, each filled with air at different pressures, are linked by a tube P that has two mercury threads inside it. The density of mercury is $13600\,\text{kg m}^{-3}$. Which pair of values for $h_1$ and $h_2$ could be correct?

Density and pressure

Which unit is used for the Young modulus?

Stress and strain

A rubber cord is suspended from a fixed support. A weight attached to its lower end is slowly increased from zero, and then slowly decreased back to zero. The force-extension curve for contraction lies below the force-extension curve for stretching. What does the shaded region between the curves represent?

Elastic and plastic behaviour

The diagram depicts a large crane at a construction site raising a cube-shaped load. A scale model is constructed of the crane, the load and the cable that supports the load. Each part of the model is made from the same material as the corresponding part of the full-size crane, cable and load. The model is one tenth full-size in every linear dimension. What is the ratio $\dfrac{\text{stress in the cable on the full-size crane}}{\text{stress in the cable on the model crane}}$?

Stress and strain

The order of magnitude for the frequency of the shortest visible-light wavelength can be written as $10^x\,\text{Hz}$. What is the value of $x$?

Electromagnetic spectrum

The diagram illustrates two waves X and Y. Wave X has amplitude $8\,\text{cm}$ and frequency $100\,\text{Hz}$. Determine the amplitude and frequency of wave Y.

Progressive waves

Which statement is true for every transverse wave?

Transverse and longitudinal waves

An electromagnetic-wave transmitter is positioned $45\,\text{cm}$ away from a reflecting surface. The waves it emits have frequency $1.00\,\text{GHz}$. A stationary wave forms with a node at the transmitter and another node at the surface. How many antinodes lie between the transmitter and the surface?

Stationary waves

A teacher assembles the apparatus illustrated to show a two-slit interference pattern on the screen. Which modification to the apparatus would make the fringe spacing larger?

Interference

A diffraction grating is illuminated at normal incidence by monochromatic light with wavelength $5.30 \times 10^{-7}\,\text{m}$. The first order maximum appears at an angle of $15.4^{\circ}$ from the direction of the incident light. What is the angle between the first and second order diffraction maxima?

The diffraction grating

As illustrated, two forces act on a circular disc. A force of $3\,\text{N}$ acts straight upwards at the top of the disc, and a force of $4\,\text{N}$ acts horizontally towards the right through the centre. Which diagram indicates the line of action of the resultant force?

Turning effects of forces

In a calculator’s liquid crystal display, the two conducting layers are $8\,\mu\text{m}$ apart. When the calculator is switched on, a $1.5\,\text{V}$ cell is connected across the conducting layers. What is the electric field strength between the layers?

Potential difference and power

A positively charged particle is launched into a uniform electric field. Which diagram shows the route followed by the particle in the electric field?

Equations of motion

A power cable is $2000\,\text{m}$ long. It consists of twelve parallel strands of copper wire, each strand having a diameter of $0.51\,\text{mm}$. Calculate the resistance of the cable. (resistivity of copper = $1.7 \times 10^{-8}\,\Omega\,\text{m}$)

Resistance and resistivity

A low-voltage source having an e.m.f. of $20\,\text{V}$ and an internal resistance of $1.5\,\Omega$ supplies a heater with resistance $6.5\,\Omega$ in a fish tank. What power is transferred to the water in the fish tank?

Potential difference and power

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

Potential difference and power

Two wires $P$ and $Q$, both formed from the same material, are attached to the same electrical supply. $P$ is twice as long as $Q$ and has one-third of the diameter of $Q$, as shown in the diagram. Determine the ratio $\dfrac{\text{current in }P}{\text{current in }Q}$?

Resistance and resistivity

A $12\,\text{V}$ battery is connected in series with an ammeter, a $2\,\Omega$ fixed resistor and a $0\! -\! 10\,\Omega$ variable resistor. High-resistance voltmeters $P$ and $Q$ are placed across the variable resistor and the fixed resistor respectively, as shown. The resistance of the variable resistor is altered from its maximum value to zero. Which graph shows how the voltmeter readings vary with current?

Potential difference and power

Five resistors are arranged as shown. Calculate the total resistance between $P$ and $Q$.

Resistance and resistivity

In the circuit shown, the voltmeter reading $V_T$ falls from high to low when the thermistor’s temperature changes. The voltmeter reading $V_L$ falls from high to low when the light intensity on the light-dependent resistor (LDR) changes. Both readings $V_T$ and $V_L$ are high. What are the temperature and light level conditions?

Practical circuits

What is the approximate mass for an alpha particle?

Atoms, nuclei and radiation

A student carried out an experiment in which an electric current was known to fall with time. The readings obtained, from first to last, were $3.62\,\text{mA}$, $2.81\,\text{mA}$, $1.13\,\text{mA}$, $1.76\,\text{mA}$ and $0.90\,\text{mA}$. Which statement would be unable to account for the anomalous $1.13\,\text{mA}$ reading?

Errors and uncertainties

An actinium nucleus has a nucleon number of $227$ and a proton number of $89$. It decays to produce a radium nucleus, with a beta particle and an alpha particle emitted in the process. What are the nucleon number and the proton number of the radium nucleus?

Atoms, nuclei and radiation

The diagram presents a thermistor calibration curve, plotted using a non-standard scale on the vertical axis. At a temperature of $40\,^{\circ}\text{C}$, what is the corresponding thermistor resistance?

Resistance and resistivity

A sky diver descends straight down from a balloon that is not moving. She separates from the balloon at time $t=0$. By time $t=T$, terminal velocity has been reached. After the interval covered by the graphs, she opens her parachute. Which graph displays how the air resistance force $F$ varies with time $t$?

Non-uniform motion

The diagram illustrates a system designed to prevent trains from going above a safe speed. Trains approaching from the left move with a speed of $50\,\text{m s}^{-1}$. At marker 1, the driver has to use the brakes so that the train slows down at a constant rate and reaches marker 2 with a speed of no greater than $10\,\text{m s}^{-1}$. The train has a detector which records the times at which it passes each marker and activates an emergency brake if the interval between passing marker 1 and marker 2 is under $20\,\text{s}$. At what distance from marker 2 should marker 1 be positioned?

Equations of motion

A ball is let go from rest above a horizontal surface and rebounds several times. The graph indicates how a quantity $y$ changes with time for this ball. What is the quantity $y$?

Equations of motion

A wall is struck by a strong wind travelling at $33\,\text{m s}^{-1}$. The air density is $1.2\,\text{kg m}^{-3}$. The wall presents an area of $12\,\text{m}^2$ perpendicular to the wind velocity. When the air reaches the wall, its speed is reduced to zero. What is the approximate force exerted by the air on the wall?

Linear momentum and its conservation

The diagram depicts a displacement vector with magnitude $5.0\,\text{km}$ at an angle of $53^\circ$ to the horizontal. What is the vertical component of this displacement vector?

Scalars and vectors

A nucleus that is initially at rest has nucleon number $A$. It undergoes decay and emits a proton with speed $v$, producing a new nucleus with speed $u$. The proton and the new nucleus travel in opposite directions, moving apart from each other. Which equation gives $v$ in terms of $A$ and $u$?

Linear momentum and its conservation

Two spheres have velocities $u_1$ and $u_2$ while moving along the same straight line. They then collide, and their velocities afterwards are $v_1$ and $v_2$. Which collision is inelastic?

Linear momentum and its conservation

The diagrams depict a negative electric charge placed in a uniform electric field and a mass placed in a uniform gravitational field. Which row indicates the directions of the forces acting on the charge and on the mass?

Scalars and vectors

A wooden block is placed on a rough board. The far end of the board is then lifted until the block moves down the surface of the board with constant velocity $v$. Which row shows the forces acting on the block while it is sliding at constant velocity?

Equilibrium of forces

A ball of mass $m$ is projected upwards through height $h$ in air with initial velocity $v$, as shown. The effect of air resistance is taken to be negligible. The acceleration of free fall is $g$. What is the total work done by the gravitational force on the ball as it travels from $P$ to $Q$?

Gravitational potential energy and kinetic energy

A spring with an unextended length of $40\,\text{mm}$ is hung from a fixed point. A load of $16\,\text{N}$ is then placed on the spring’s free end. As a result, the spring stretches until its final length becomes five times its original length. The spring follows Hooke’s Law. What is the energy stored in the spring due to this extension?

Elastic and plastic behaviour

The diagram illustrates a setup that is used to determine the output power of an electric motor. The wheel fixed to the motor’s axle has a circumference of $0.5\,\text{m}$, and the belt passing over it is at rest 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?

Gravitational potential energy and kinetic energy

Ice at a temperature of $0^{\circ}\text{C}$ is an unusual solid because it floats on its liquid form, water, when both are at the same temperature. What explains this?

Density and pressure

The hydrostatic pressure formula is $p = \rho g h$. Which equation, or principle of physics, is applied in deriving this formula?

Density and pressure

The diagram depicts a large construction-site crane raising a cube-shaped load. A scale model is formed of the crane, the load and the cable that holds the load. Each part of the model is made from the same material as the corresponding part in the actual crane, cable and load. In the model, every linear dimension is one tenth of the full-size version. What is the ratio $\frac{\text{extension of the cable on the full-size crane}}{\text{extension of the cable on the model crane}}$?

Stress and strain

In SI base units, what is the unit for power?

SI units

Which graph shows the force-extension relationship for a rubber band when it is stretched to nearly the point of breaking?

Elastic and plastic behaviour

A spring is extended across a range for which elastic deformation takes place. Its spring constant is $3.0\,\text{N cm}^{-1}$. Which row gives the correct extension and strain energy for the stated applied force?

Elastic and plastic behaviour

Which statement concerning the various types of electromagnetic wave is correct?

Electromagnetic spectrum

Orange light has a wavelength of $600\,\text{nm}$. Determine the frequency of this light.

Electromagnetic spectrum

Electromagnetic waves of wavelength $\lambda$ and frequency $f$ travel at speed $c$ in a vacuum. Which statement describes the wavelength and speed of electromagnetic waves of frequency $f/2$?

Electromagnetic spectrum

When a calculator's liquid crystal display is viewed through a polarising film, the appearance of the display varies as the film is turned. Which property of the radiation from the calculator display is being described?

Polarisation

For a sound wave, the displacement is $y$ at a distance $x$ from the source at time $t$. Which graph shows the amplitude $a$ and the wavelength $\lambda$ of the wave correctly?

Progressive waves

Red light in a parallel beam with wavelength $700\,\text{nm}$ falls normally on a diffraction grating with $400$ lines per millimetre. How many transmitted maxima are there in total?

The diffraction grating

The diagram illustrates a standing wave on a string. There are three nodes on the standing wave, $N_1$, $N_2$ and $N_3$. Which statement is correct?

Stationary waves

Two metal plates are positioned horizontally and parallel to each other, $5.0\,\text{cm}$ apart. The plates have potentials of $+100\,\text{V}$ and $+20\,\text{V}$. What force acts on an electron within the electric field between the plates?

Potential difference and power

Which statement is wrong by a factor of $100$ or more?

Errors and uncertainties

The diagram illustrates the trajectory of a charged particle in a uniform electric field, with vertical field lines. What might produce a path of this form?

Equations of motion

Cells $X$ and $Y$ are joined in series with a resistor of resistance $9.0\,\Omega$, as shown. Cell $X$ has an electromotive force (e.m.f.) of $1.0\,\text{V}$ and an internal resistance of $1.0\,\Omega$. Cell $Y$ has an e.m.f. of $2.0\,\text{V}$ and an internal resistance of $2.0\,\Omega$. What current flows in the circuit?

Practical circuits

The cross-sectional area of a metal wire is circular and changes as you move along its length. A current flows through the wire. The thinner end of the wire is at a reference potential taken as zero. Which graph most accurately shows how the potential difference $V$, relative to the zero reference, varies with distance $x$ along the wire?

Potential difference and power

The graph illustrates the way current $I$ depends on voltage $V$ for a filament lamp. Because the graph is not a straight line, the lamp's resistance changes with $V$. Which row gives the correct resistance for the stated value of $V$?

Resistance and resistivity

An electric power cable is made up of six copper wires $c$ that surround a steel core $s$. For a $1.0\,\text{km}$ section of one copper wire, the resistance is $10\,\Omega$ and, for a $1.0\,\text{km}$ section of the steel core, the resistance is $100\,\Omega$. What is the approximate resistance of a $1.0\,\text{km}$ section of the power cable?

Resistance and resistivity

The figure depicts a length of model-railway track connected to a battery, a resistor and a relay coil. When no train is on the track, current flows in the relay coil, which makes a switch operate and turn on a light. When a train is in that section of track, most of the current travels through the train’s wheels and axles instead of through the relay coil. The switch in the relay then turns off the light. What is the reason for fitting a resistor between the battery and the track?

Resistance and resistivity

An ammeter, a $2\,\Omega$ fixed resistor and a $0\text{-}10\,\Omega$ variable resistor are connected in series with a $12\,\text{V}$ battery. A high-resistance voltmeter is connected across the fixed resistor. The resistance of the variable resistor is then altered from zero to its maximum value. Which graph shows the way the potential difference (p.d.) recorded by the voltmeter changes with the current recorded by the ammeter?

Resistance and resistivity

In the circuit illustrated, the battery and the ammeter each have negligible resistance. The resistor combinations below are connected one after another between terminals $X$ and $Y$ in the circuit. Which combination would produce an ammeter reading of $8\,\text{A}$?

Practical circuits

Scientists studying the count rate from a radioactive source noticed that the count rate varies. What do these variations indicate about the nature of radioactive decay?

Atoms, nuclei and radiation

When a nucleus of neptunium decays, a $\beta$-particle and $\gamma$-radiation are emitted. What change, if any, does this decay cause to the proton number and to the nucleon number of the nucleus?

Atoms, nuclei and radiation

A cyclist is moving directly south with velocity $u$. The wind is coming from the north-east with velocity $w$. The wind’s velocity relative to the cyclist is $v$, where $v = w - u$. Which vector diagram indicates the size and direction of velocity $v$?

Scalars and vectors

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

Atoms, nuclei and radiation

A student records the current through a resistor with constant resistance and the potential difference (p.d.) across it. The data are then used to produce a graph of current against p.d. The current readings include a systematic error. How could this be identified from the graph?

Resistance and resistivity

The diagram shows the stem of a Celsius thermometer, with markings indicating the initial and final temperature readings. What is the temperature change, written to an appropriate number of significant figures?

Errors and uncertainties

A double-ended launching device sends two identical steel balls $X$ and $Y$ out at precisely the same time. The diagram indicates the balls’ initial velocities. Both are projected horizontally, although $Y$ has the larger speed. Which statement best explains what an observer would see?

Equations of motion

At time $t = 0$, a body starts from rest and travels in a straight line with constant acceleration. When the time is $t$, the body is at a distance $s$ from its rest position. A graph of $s$ against $t^{2}$ is plotted, as shown. Which statement gives the acceleration of the body?

Equations of motion

A lift (elevator) has a passenger car that is held up by a cable passing over a light, frictionless pulley and attached to a balancing weight. As the passenger car moves upward, the balancing weight descends. The table lists some masses: Passenger car: $520\,\text{kg}$ Balancing weight: $640\,\text{kg}$ Passenger: $80\,\text{kg}$ When the car is carrying only one passenger and the pulley is free to rotate, what is the magnitude of the car’s acceleration?

Momentum and Newton's laws of motion