May/June 2016

As illustrated, three wires each apply a horizontal force to a vertical pole. Which vector diagram represents the resultant force $R$ on the pole?

Scalars and vectors

Two spheres move towards one another along the same straight line. Before they collide, their speeds are $u_1$ and $u_2$. Once the collision is over, the spheres move apart with speeds $v_1$ and $v_2$ in the directions shown below. The collision is perfectly elastic. Which equation must be correct?

Linear momentum and its conservation

The diagram depicts a man on a platform connected to a flexible pipe. Water is forced through the pipe so that the man and platform stay at the same height. The net vertical force acting on the platform is zero. The total mass of the man and platform is $96\,\text{kg}$. Each second, $40\,\text{kg}$ of water is expelled vertically downward from the platform. What is the speed of the water as it leaves the platform?

Linear momentum and its conservation

A rigid body is acted on by forces. All of the forces lie in one plane. Which diagram shows the body in equilibrium?

Equilibrium of forces

A solid metal cylinder is placed on a horizontal surface, as illustrated. The cylinder has length $x$ and cross-sectional area $A$. The cylinder produces a pressure $p$ on the surface. The acceleration of free fall is $g$. Which expression gives the density of the metal in the cylinder?

Density and pressure

A trailer with weight $30\,\text{kN}$ is connected to a cab at $X$, as shown in the diagram. What upward force does the cab exert on the trailer at $X$?

Equilibrium of forces

A micrometer screw gauge is used to measure the diameter of a solid metal sphere. The diagram gives a magnified view of the shaft of the micrometer screw gauge as the measurement is being taken. The sphere has a mass of $0.450\,\text{g}$. What is the density of the metal from which the sphere is made?

Density and pressure

A gas inside a cylinder receives thermal energy $q$. As it expands at constant pressure $p$, the gas performs useful work as its volume changes from $V_0$ to $V_F$, as illustrated. Which expression gives the efficiency of this change?

Energy conservation

The power $P$ needed to move an object through a medium at constant speed is determined by the speed $v$ and the resistive force $F$ acting on the object. The resistive force $F$ is also determined by the speed $v$. Which row gives a possible relationship between speed $v$, resistive force $F$ and power $P$?

Energy conservation

Which energy value is not $2400\,\text{J}$?

SI units

A hammer carrying $10\,\text{J}$ of kinetic energy strikes a nail and drives it $5.0\,\text{mm}$ into a plank. After the impact, both the hammer and the nail are at rest. What is the approximate average force acting on the nail during the $5.0\,\text{mm}$ penetration?

Energy conservation

Which pair of quantities has different SI base units?

SI units

Several identical springs are connected in four different arrangements. Which arrangement has the same spring constant as one spring?

Elastic and plastic behaviour

A sample of material is pulled by a tensile force until it has moved past its elastic limit. The tensile force is then reduced to zero. The graph of force against extension is shown. Which area shows the net work done on the sample?

Elastic and plastic behaviour

Two sound waves have frequencies of $250\,\text{Hz}$ and $300\,\text{Hz}$. The speed of sound is $340\,\text{m s}^{-1}$. What is the difference in wavelength between these two waves?

Progressive waves

Which electromagnetic waves correspond to wavelengths of $10^{-2} \text{m}$, $10^{-5} \text{m}$, $10^{-10} \text{m}$ and $10^{-13} \text{m}$?

Electromagnetic spectrum

Which of the following statements about a stationary wave is correct?

Stationary waves

Continuous water waves pass through a gap in a barrier in a ripple tank and are diffracted. Which change would make the diffraction of the waves greater?

Diffraction

A parallel beam of light with wavelength $450\,\text{nm}$ falls normally on a diffraction grating that has $300$ lines $\text{mm}^{-1}$. What is the total number of intensity maxima that are observed?

The diffraction grating

A screen $1.00\,\text{m}$ from a double slit shows fringes with spacing $x$ when the slits are illuminated by yellow light of wavelength $600\,\text{nm}$. At what distance from the slits should the screen be placed so that blue light of wavelength $400\,\text{nm}$ produces fringes with the same spacing $x$?

Interference

A charged particle is travelling through a uniform electric field. During the particle’s motion caused by the field, which quantity remains at a constant non-zero value?

Equations of motion

Which diagram could show the electric field lines between two conducting surfaces with opposite charges?

Scalars and vectors

A lift is held up by two steel cables, each with length $10\,\text{m}$ and diameter $0.5\,\text{cm}$. When a man with mass $80\,\text{kg}$ gets into the lift, the cables lengthen by $1\,\text{mm}$. What is the best estimate for the Young modulus of the steel?

Stress and strain

A resistor carries a current for an unknown length of time. Which two quantities can be used to determine the energy dissipated by the resistor?

Potential difference and power

A pair of copper wires with the same length are joined in parallel. A potential difference is applied across the two ends of this parallel arrangement. Wire S has a diameter of $3.0\,\text{mm}$. Wire T has a diameter of $1.5\,\text{mm}$. What is the value of the ratio $\dfrac{\text{current in S}}{\text{current in T}}$?

Resistance and resistivity

A $100\,\Omega$ resistor carries a current whose direction and magnitude vary, as shown. What is the average power dissipated in the resistor?

Potential difference and power

Which graph displays the $I$-$V$ characteristic of a filament lamp?

Resistance and resistivity

For the circuit diagram shown, $X$ is a variable resistor, and its resistance may be adjusted from $5.0\,\Omega$ to $500\,\Omega$. The e.m.f. of the battery is $12.0\,\text{V}$. It has negligible internal resistance. What is the greatest range of values of potential difference across the output?

Potential dividers

A current flows from P to R through the resistor network shown. The potential difference (p.d.) between P and Q is $3\,\text{V}$. The p.d. between Q and R is $6\,\text{V}$. The p.d. between P and S is $5\,\text{V}$. Which row in the table is correct?

Kirchhoff's laws

A pair of resistors with resistances $R_1$ and $R_2$ are joined in parallel. What is the total resistance between X and Y?

Resistance and resistivity

A voltmeter is employed to observe how an electric motor is working. The motor’s speed is adjusted using a variable resistor. A fixed resistor is included to restrict the speed. The current in the motor is slowly varied. In which circuit does the voltmeter reading vary in proportion to the current in the motor?

Practical circuits

Which statement gives a description of $\beta^-$ decay in a simple quark model?

Fundamental particles

Which word equation shows $\beta^+$ decay?

Atoms, nuclei and radiation

When carrying out an experiment, a student should reduce the uncertainty in every measurement as much as possible. In which situation is the student lowering the systematic error in a measurement?

Errors and uncertainties

Which statement about the alpha-particle scattering experiment gives evidence that the nucleus exists?

Atoms, nuclei and radiation

A calibration graph has been drawn for a faulty ammeter. Which ammeter reading is closest to the true current?

Practical circuits

A car speeds up with uniform acceleration from velocity $u$ to velocity $v$ over a time interval of $t$. On the graph, which area is equal to the distance the car travels in time $t$?

Equations of motion

A student uses a spring gun to fire a steel ball with a constant horizontal velocity. He changes the height $h$ of the gun and records the horizontal displacement $r$ of the ball as it lands on the ground. Which graph shows how the horizontal displacement $r$ varies with height $h$?

Equations of motion

At time $t = 0$, cars X and Y are located as illustrated. Both are moving in the same direction. X is $50\,\text{m}$ behind Y and moves with a constant velocity of $30\,\text{m s}^{-1}$. Y moves with a constant velocity of $20\,\text{m s}^{-1}$. What is the value of $t$ when X is level with Y?

Equations of motion

Which statement about a perfectly elastic collision between two bodies in an isolated system is correct?

Linear momentum and its conservation

Which quantity, together with its unit, is correct?

SI units

A sphere is released from rest and falls through the air. The graph shows how the sphere’s velocity changes with time. Which diagram represents the forces acting on the sphere when its velocity is the one at point $P$ on the graph?

Momentum and Newton's laws of motion

A ball of mass $m$ moving with velocity $u$ collides with a second ball of mass $M$ that is initially at rest. After the collision, the two balls move with velocities $v$ and $V$ respectively, in the directions shown. A student then writes three equations for the collision. Which row in the table shows which equations are correct and which are incorrect? Equations: 1. $mu = M V + m v$ 2. $m v \sin 30^{\circ} = M V \sin 40^{\circ}$ 3. $mu = m v \cos 30^{\circ} + M V \cos 40^{\circ}$

Linear momentum and its conservation

A light rigid rod $XY$ has an object of weight $W$ attached at one end. The rod is balanced, with support from a roller at $Z$ and a vertical wall at $X$. The roller provides a force $R$ on the rod, as shown. The diagram indicates the directions, but not the sizes, of the forces $R$ and $W$. What is the direction of the force acting on the rod at $X$?

Equilibrium of forces

Inside a large tank at an oil refinery, three oils with different densities are blended together. There is no chemical reaction. The mixture contains $1200\,\text{kg}$ of oil with density $1100\,\text{kg m}^{-3}$, $1500\,\text{kg}$ of oil with density $860\,\text{kg m}^{-3}$, $4000\,\text{kg}$ of oil with density $910\,\text{kg m}^{-3}$. Determine the density of the mixture.

Density and pressure

Two coplanar forces act at the edge of a wheel. The forces have equal magnitudes. Which arrangement of forces produces only a couple?

Turning effects of forces

The density of air in the Earth’s atmosphere falls by almost a straight-line relationship as height increases, dropping from $1.22\,\text{kg m}^{-3}$ at sea level to $0.74\,\text{kg m}^{-3}$ at an altitude of $5000\,\text{m}$. On a certain day, the atmospheric pressure at the Earth’s surface is $100\,000\,\text{Pa}$. Over the region from the Earth’s surface up to an altitude of $5000\,\text{m}$, $g$ may be taken as constant at $9.7\,\text{m s}^{-2}$. What is the atmospheric pressure at an altitude of $5000\,\text{m}$?

Density and pressure

A parachutist is descending at a constant (terminal) velocity. Which statement is incorrect?

Momentum and Newton's laws of motion

A boy riding a bicycle begins from rest and moves down a hill that is inclined at $30^\circ$ to the horizontal. The boy together with the bicycle has a total mass of $25\,\text{kg}$. A frictional force of $30\,\text{N}$ acts, and this force does not depend on the bicycle’s velocity. What is the kinetic energy of the boy and the bicycle after they have travelled $20\,\text{m}$ down the slope?

Energy conservation

In an underground station, an escalator is carrying $250$ people while moving at a velocity of $4.3\,\text{m s}^{-1}$. The mean mass of one person is $78\,\text{kg}$, and the escalator is inclined at an angle of $40^\circ$ to the horizontal. What minimum power is needed to raise these people?

Gravitational potential energy and kinetic energy

An electric motor that drives a lift delivers an output power of $20\,\text{kW}$. The lift together with its passengers has a total mass of $1500\,\text{kg}$. The motor lifts the lift by a vertical distance of $20\,\text{m}$. How long is required?

Gravitational potential energy and kinetic energy

The luminosity $L$ of a star is defined by $L = 4\pi r^2 \sigma T^4$, where $r$ represents the star's radius, $T$ denotes the star's temperature, and $\sigma$ is a constant with units $\text{W m}^{-2}\,\text{K}^{-4}$. What are the SI base units of $L$?

SI units

A spring balance is made from a spring that has an initial length of $20.0\,\text{cm}$ and a hook fixed to it. When a fish with mass $3.0\,\text{kg}$ is hung from the hook, the spring’s length increases to $27.0\,\text{cm}$. What is the spring constant of the spring?

Stress and strain

A metal wire has one end secured to a fixed point, while a load is suspended from the opposite end so that the wire hangs straight down. The load is then raised from zero to $20\,\text{N}$. As a result, the wire undergoes an elastic extension of $5.0\,\text{mm}$. Next, the load is lowered to $12\,\text{N}$, and the extension falls to $3.0\,\text{mm}$. How much strain energy is released as the wire is unloaded?

Elastic and plastic behaviour

A microphone linked to the Y-plates of a cathode-ray oscilloscope (c.r.o.) is positioned in front of a loudspeaker. The c.r.o. screen shows the trace. The time-base setting is $0.5\,\text{ms cm}^{-1}$ and the Y-plate sensitivity is $0.2\,\text{mV cm}^{-1}$. What is the frequency of the sound produced by the loudspeaker and what is the amplitude of the trace on the c.r.o.?

Progressive waves

A source producing sound with frequency $1000\,\text{Hz}$ travels away from an observer who is at rest at a speed of $30.0\,\text{m s}^{-1}$. The speed of sound is $330\,\text{m s}^{-1}$. What frequency of sound does the observer hear?

Doppler effect for sound waves

Every main region in the electromagnetic spectrum covers a particular span of wavelengths. Which wavelength is matched correctly with its radiation?

Electromagnetic spectrum

A stationary wave is formed on a stretched string. The diagram depicts the string at two separate moments when its displacement is greatest. Point $P$ on the string oscillates with amplitude $A$. How far does $P$ travel from the position shown in the diagram after half a time period of the wave?

Stationary waves

Which statement gives an example of light diffraction?

Diffraction

Sound waves with wavelength $\lambda$ are produced by a loudspeaker and travel through two slits $P$ and $Q$. Two sound waves from these slits arrive together at $R$. What condition must be met for a microphone at $R$ to detect an intensity maximum (loud sound)?

Interference

Coherent light is sent through a double slit, creating bright and dark fringes on a screen positioned parallel to the plane of the double slit. At first, the light intensity from each slit is equal. The intensity of the light passing through one slit in the double slit is then increased. The frequency of the light stays constant. What effect does this have on the appearance of the fringes on the screen?

Interference

Which diagram illustrates the arrangement of the electric field between a positively charged metal sphere and a negatively charged metal plate?

Potential difference and power

The diagram illustrates two vectors $X$ and $Y$, drawn to scale. If $X = Y - Z$, which diagram most accurately shows vector $Z$?

Scalars and vectors

Just before a thunderstorm, the hairs on your head may occasionally stand up. A hair with mass $0.50\,\text{mg}$ and charge $1.0\,\text{pC}$ is held in equilibrium by a force produced by an electric field. Ignore all forces apart from the weight of the hair and the electric force. Find the electric field strength?

Equilibrium of forces

Two parallel metal plates, $4.0\,\text{cm}$ apart, have electric potentials of $800\,\text{V}$ and $2000\,\text{V}$. Points X, Y and Z lie in the region between the plates at distances of $1.0\,\text{cm}$, $2.0\,\text{cm}$ and $3.0\,\text{cm}$ from the lower plate. Calculate the electric field strength, in $\text{V m}^{-1}$, at X, Y and Z?

Potential difference and power

The potential difference $V$ across a filament lamp is gradually increased from zero until it reaches its normal operating value. Which graph shows how the current $I$ in the lamp varies with $V$?

Resistance and resistivity

Two lamps are joined in series to a $250\,\text{V}$ power supply. One lamp has a rating of $240\,\text{V},\,60\,\text{W}$ and the other has a rating of $10\,\text{V},\,2.5\,\text{W}$. Which statement gives the best description of the result?

Potential difference and power

Which equation is used to express resistance?

Resistance and resistivity

The amount of charge a fully charged $12\,\text{V}$ car battery can provide is $100\,\text{kC}$. The starter motor of the car needs a current of $200\,\text{A}$ for an average time of $2.0\,\text{s}$. A fault means the battery does not recharge. What is the greatest number of times the starter motor of the car can be operated?

Electric current

A potential divider circuit is made by linking a battery with negligible internal resistance in series with two variable resistors, as illustrated. The variable resistors have resistances $R_x$ and $R_Y$. $V_x$ is the potential difference across resistance $R_x$. $R_x$ and $R_Y$ are both altered at the same time. Which set of changes must make $V_x$ increase?

Potential dividers

In the circuit diagram shown, contact can be made at any position along the $3\,\Omega$ resistor (potentiometer). The battery has e.m.f. $9\,\text{V}$ and negligible internal resistance. What is the greatest possible range of the output voltage?

Potential dividers

The gold nucleus $^{{185}}_{{79}}\text{Au}$ is decaying by alpha emission. What are the nucleon number and proton number of the nucleus produced in this decay?

Atoms, nuclei and radiation

Which row correctly classifies protons, electrons and neutrinos?

Fundamental particles

The diagram illustrates a cathode-ray oscilloscope (c.r.o.) being used to determine the rotation rate of a flywheel. A small magnet is attached to the flywheel. Whenever the magnet moves past the coil, a voltage pulse is produced and then sent to the c.r.o. The width of the c.r.o. display is $10\ \text{cm}$. The flywheel is turning at $3000$ revolutions per minute. Which time-base setting will show pulses that are clearly separated on the screen?

Practical circuits

Which equation shows $\beta^+$ decay?

Atoms, nuclei and radiation

A student works out the density $\rho$ of steel from measurements made on a steel wire. mass $m = 6.2 \pm 0.1\ \text{g}$ length $l = 25.0 \pm 0.1\ \text{cm}$ diameter $d = 2.00 \pm 0.01\ \text{mm}$ He uses the equation $\rho = \frac{4m}{\pi d^2 l}$. Calculate the percentage uncertainty in his calculated value of density?

Errors and uncertainties

The acceleration of free fall on the Moon is $1.6\ \text{m s}^{-2}$. There is no atmosphere on the Moon. An astronaut on the Moon’s surface lets go of a feather. Which graph shows how the feather’s speed changes with time during the first second of its fall?

Equations of motion

A tennis ball is let go from rest at the top of a tall building. Which graph most accurately shows how the acceleration $a$ of the ball changes with time $t$ as it falls, assuming that air resistance has a noticeable effect?

Non-uniform motion

The graph illustrates how the velocity $v$ of an object moving in a straight line changes with time $t$ over the interval from $t = 0$ to $t = T$. Which graph shows the displacement $s$ of the object for the time interval $t = 0$ to $t = T$?

Equations of motion

A ball drops straight down onto a horizontal surface and bounces back, as illustrated. Just before it strikes the ground, the ball has momentum $p_1$ downwards. Once it has rebounded, it moves away from the ground with momentum $p_2$ upwards. The ball remains in contact with the ground for $0.020\,\text{s}$. Over this time interval, an average resultant force of $25\,\text{N}$ acts on the ball. What is a possible combination of values for $p_1$ and $p_2$?

Momentum and Newton's laws of motion

Which list includes only SI base units?

SI units

Two equal masses move towards one another along a frictionless track with speeds of $60\,\text{cm s}^{-1}$ and $30\,\text{cm s}^{-1}$. On collision, they remain stuck together. What is the speed of the masses after impact?

Linear momentum and its conservation

The IKAROS satellite has a mass of $320\,\text{kg}$ and travels through space by means of a solar sail with area $20\,\text{m}^2$. The mean solar wind pressure is $1.0 \times 10^{-5}\,\text{N m}^{-2}$. What acceleration does the solar wind produce on the satellite?

Momentum and Newton's laws of motion

An object is acted on by three coplanar forces in the directions shown. Which diagram shows a possible equilibrium situation for the object?

Equilibrium of forces

What is meant by the centre of gravity of an object?

Turning effects of forces

As shown, a bicycle pedal is joined to a pivot by a metal bar. A downward force of $60\,\text{N}$ acts on the pedal. What moment does this force produce about the pivot?

Turning effects of forces

For a change in depth $\Delta h$ within a liquid of density $\rho$, the corresponding change in pressure $\Delta p$ is given by $\Delta p = \Delta h\rho g$, where $g$ represents the acceleration of free fall. Which equation, or principle of physics, is used to derive this formula?

Density and pressure

A bungee jumper leaps from a platform and is slowed down by an elastic bungee cord, as illustrated. As the jumper begins the jump, his initial gravitational potential energy is changed into kinetic energy and elastic potential energy in the cord. During which part of the jump are all three forms of energy non-zero?

Energy conservation

A body of mass $0.30\,\text{kg}$ is projected vertically upwards from the ground with an initial speed of $8.0\,\text{m s}^{-1}$. It attains a greatest height of $1.9\,\text{m}$. Determine how much work is done against air resistance while the body rises to this maximum height?

Energy conservation

A racing car develops an output power of $300\,\text{kW}$ while moving at a constant speed of $60\,\text{m s}^{-1}$. Determine the total resistive force on the car.

Energy conservation

The diagram illustrates the design of a water wheel that turns a generator to generate electrical power. The flow rate of the water is $200\,\text{kg s}^{-1}$. The generator provides a current of $32\,\text{A}$ at a voltage of $230\,\text{V}$. If any change in the kinetic energy of the water is ignored, what is the efficiency of the system?

Gravitational potential energy and kinetic energy

The stress $\sigma$ required to break a certain solid is described by $\sigma = k \sqrt{\frac{\gamma E}{d}}$, where $E$ represents the Young modulus, $d$ is the separation between atomic planes, and $k$ is a constant with no units. What are the SI base units of $\gamma$?

Stress and strain

The graph illustrates the force-extension relationship for a sample of material. The sample is stretched and then goes back to its starting length. Which area shows the work done in stretching the sample?

Elastic and plastic behaviour

A metal wire with cross-sectional area $0.20\,\text{mm}^2$ is suspended vertically from a fixed point. An $84\,\text{N}$ load is then added to its lower end. The wire follows Hooke’s law and its length increases by $0.30\%$. What is the Young modulus of the metal in the wire?

Stress and strain

The diagram illustrates a beam resting on two pivots. Which statement describes the condition of the upper surface X and the lower surface Y?

Turning effects of forces

A red laser beam is $1.0\,\text{m}$ long. What is the order of magnitude of the number of wavelengths of the red light in $1.0\,\text{m}$?

Electromagnetic spectrum

As a car moving at constant velocity passes an observer at rest, the observer notices a change in the frequency of the sound produced by the car. Which statement is correct?

Doppler effect for sound waves

The sound intensity $I$ varies inversely with the square of the distance $x$ from the sound source. This is expressed as $I \propto \frac{1}{x^2}$. At point P, which is a distance $r$ from the source S, air molecules oscillate with an amplitude of $8.0\,\mu\text{m}$. Point Q is located a distance $2r$ from S. Determine the oscillation amplitude of the air molecules at Q.

Progressive waves

A hill lies between a television (TV) transmitter and a house, so the transmitter cannot be seen from the house. Even so, the house receives a good TV signal. Which wave effect at the hill allows the TV signal to reach the house?

Diffraction

A diffraction grating with $N$ lines per metre is used to deflect light of different wavelengths $\lambda$. The graph plots the relationship between the deflection angle $\theta$ and $\lambda$ for a range of wavelengths in the $n^{\text{th}}$ order interference pattern. What is the gradient of the graph?

The diffraction grating

Which wave phenomenon is not required to account for the pattern of observable fringes formed in a double slit experiment?

Interference

Which diagram illustrates the electric field pattern around an isolated negative point charge?

Potential difference and power

Vectors $P$ and $Q$ have been drawn to scale. Which diagram shows the vector $(P - Q)$?

Scalars and vectors

An electron is placed in an electric field of strength $5 \times 10^4\,\text{V m}^{-1}$. No other force acts on the electron. The mass and charge of an electron are known. Which quantity can be worked out without any additional information?

Momentum and Newton's laws of motion

Within an electrolyte, electric current is carried by charged particles (ions) dissolved in the solution. Which value cannot be the charge on an ion in solution?

Atoms, nuclei and radiation

The graph illustrates how the resistance of a uniform metal wire changes as its length changes. The graph’s gradient is $G$. The wire has cross-sectional area $A$. Which expression could be used to calculate the resistivity of the metal in the wire?

Resistance and resistivity

What term describes the electric potential difference across two points in a current-carrying wire?

Potential difference and power

Possible current-voltage ($I$-$V$) characteristics for a filament lamp and a semiconductor diode are shown in the graphs. Which row in the table gives the correct $I$-$V$ graphs for the lamp and for the diode?

Resistance and resistivity

In a circuit there are a cell, two resistors with resistances $R_1$ and $R_2$, and a variable resistor $X$. The cell is assumed to have negligible internal resistance. $V_1$ denotes the potential difference across the resistor of resistance $R_1$. $I_2$ denotes the current through the resistor of resistance $R_2$. The resistance of $X$ is decreased. What effect does this have on $V_1$ and $I_2$?

Potential dividers

A $100\,\text{cm}$ potentiometer wire $QT$ is arranged in series with a $2.00\,\text{V}$ cell. A second circuit, made up of a $2.00\,\text{V}$ cell in series with resistors of resistance $4.00\,\Omega$ and $6.00\,\Omega$, is placed beside the potentiometer. The links $PQ$ and $RS$ are then connected so that the potential difference (p.d.) across the $4.00\,\Omega$ resistor is matched with the p.d. across a length $L$ of potentiometer wire. Both cells are assumed to have negligible internal resistance. What is the balance length $L$?

Potential dividers

Two batteries that are identical each have e.m.f. $6.0\,\text{V}$ and internal resistance $r$. As illustrated, the batteries are linked to an external resistor with resistance $11\,\Omega$. The current through the external resistor is $0.50\,\text{A}$. What is the value of the internal resistance $r$ for each battery?

Practical circuits

A nitrogen-13 nucleus $^{13}_{7}\text{N}$ decays by beta emission. In the equations shown below, $\nu$ and $\bar{\nu}$ denote a neutrino and an antineutrino respectively, while $\gamma$ stands for a photon of gamma radiation. Which equation shows this decay?

Atoms, nuclei and radiation

Radon $^{222}_{86}\text{Rn}$ begins a decay series that produces bismuth $^{214}_{83}\text{Bi}$ through $\alpha$ and $\beta^-$ emissions. During the decay of each radon nucleus, how many $\alpha$ particles and how many $\beta^-$ particles are emitted?

Atoms, nuclei and radiation

The diagram shows a metre rule resting horizontally on two pivots. The vertical displacement $y$ at the centre of the rule is related by $y = \dfrac{kML^3}{wt^3}$ where $k$ is a constant, $L$ is the separation between the pivots, $M$ is the mass of the rule, $t$ is the thickness of the rule and $w$ is the width of the rule. In an experiment, these values are measured: $L = (80.0 \pm 0.2)\,\text{cm}$ $M = (60 \pm 1)\,\text{g}$ $t = (6.0 \pm 0.1)\,\text{mm}$ $w = (23.0 \pm 0.5)\,\text{mm}$ Which measurement makes the largest contribution to the uncertainty in the calculated value of $y$?

Errors and uncertainties

The proton’s charge can be taken to have a size of $+1$ unit. With this convention, the charges of the up ($u$) quark, down ($d$) quark and their antiquarks ($\bar{u}$ and $\bar{d}$) are not whole units. Which row in the table gives the correct values for the charges of the $u$, $d$, $\bar{u}$ and $\bar{d}$ quarks?

Fundamental particles

The trace below is displayed on the cathode-ray oscilloscope screen. The time-base setting is then altered from $10\,\text{ms cm}^{-1}$ to $20\,\text{ms cm}^{-1}$, while the Y-plate sensitivity stays unchanged. Which trace is displayed on the screen now?

Practical circuits

A ball moves in a straight line up a ramp and then returns down the ramp along the same route. Which graph shows how the ball’s velocity changes with time?

Equations of motion

A ball is projected with velocity $V$ at an angle $\theta$ above the horizontal. The acceleration due to free fall is $g$. Take air resistance to be negligible. What are the horizontal displacement $x$ and the vertical displacement $y$ after time $t$?

Equations of motion

A ball moves from point X to point Y along a semi-circular track of radius $1.0\,\text{m}$, as illustrated. What is the ball's displacement from X to Y?

Scalars and vectors

Which line in the table shows the quantities that remain conserved in a perfectly elastic collision between two gas molecules?

Linear momentum and its conservation