Oct/Nov 2015

Which SI base unit(s) are used to express weight?

SI units

A golf ball is struck by a club. The graph shows how the force exerted by the club on the ball varies with time. Which quantity, for the period of contact, cannot be determined from the graph?

Momentum and Newton's laws of motion

A glider with mass $1500\,\text{kg}$ is set off from rest along a straight, level track by means of a catapult. The graph illustrates how the resultant force changes with time. What is the glider’s speed at the instant the resultant force on it becomes zero?

Momentum and Newton's laws of motion

Which statement is always correct about a ball that hits a tennis racket and bounces back?

Momentum and Newton's laws of motion

In which example would it be impossible for the underlined body to be in equilibrium?

Equilibrium of forces

Two blocks X and Y are falling in a vacuum within a uniform gravitational field, as illustrated. Block X has weight $2w$. Block Y has weight $w$. The blocks do not separate. Which value most nearly represents the force exerted by block X on block Y?

Momentum and Newton's laws of motion

A gas is trapped in a sealed syringe, as illustrated. The gas volume at room temperature is $2.0\,\text{cm}^3$. Atmospheric pressure is $101\,\text{kPa}$. What is the work done by the gas as it is heated and expands to a volume of $6.0\,\text{cm}^3$?

Density and pressure

A combined heat and power (CHP) station produces electrical power together with useful heat. The diagram illustrates the input and output of a CHP station. What is the efficiency of the CHP station in producing useful power?

Energy conservation

An electric car can travel $150\,\text{km}$ in ‘normal driving conditions’. In doing so, it consumes all of the $200\,\text{MJ}$ stored in its batteries. The batteries are first fully charged, and then the car is driven for $100\,\text{km}$ in ‘normal driving conditions’. After that, the batteries are recharged using a household electrical supply that provides a constant current of $13.0\,\text{A}$ at a potential difference (p.d.) of $230\,\text{V}$. What is the minimum time required to recharge the batteries?

Potential difference and power

A fixed quantity of gas is compressed so that its volume decreases while the temperature stays constant. Why does the pressure of the gas increase?

Atoms, nuclei and radiation

Mercury fills a U-tube that is sealed at one end. Air, at a pressure of $5.0 \times 10^4\,\text{Pa}$, is trapped in the closed end. The opposite end is exposed to the atmosphere and has a piston of mass $5.0\,\text{kg}$ and cross-sectional area $5.0 \times 10^{-4}\,\text{m}^2$. The density of mercury is $13\,600\,\text{kg m}^{-3}$ and atmospheric pressure is $1.01 \times 10^5\,\text{Pa}$. Determine the height $h$ of the mercury column.

Density and pressure

When the temperature is very near $0\,\text{K}$, the specific heat capacity of a certain solid obeys $c = bT^{3}$, with $T$ representing the thermodynamic temperature and $b$ being a constant for that solid. The SI unit for specific heat capacity is $\text{J kg}^{-1}\text{K}^{-1}$. What is the unit of constant $b$, written in SI base units?

SI units

A known tensile force is applied to a wire. The wire stays below its elastic limit. Which two measurements are needed to calculate the strain of the wire?

Stress and strain

The Young modulus of steel is measured with a steel wire of length and is found to be $E$. A second experiment is then performed with a wire made of the same steel, but with half the length and half the diameter. What value is obtained for the Young modulus in the second experiment?

Stress and strain

The graph illustrates how the strain of a material changes with stress as it is stretched elastically. Why is the strain energy per unit volume of the material not equal to the area beneath the graph?

Stress and strain

A wire ends up with a length of $6.0\ \text{m}$ after experiencing a strain of $200\%$. What was the wire’s original length?

Stress and strain

A sound wave is shown on the screen of a cathode-ray oscilloscope, as illustrated. The time-base setting is $0.50\ \text{ms}$ per division. What is the frequency of the sound wave?

Progressive waves

A section of a car was heat-damaged because, on a bright day, it had been parked opposite a curved building with mirrors that concentrated reflected sunlight onto the vehicle. Which statement about sunlight gives the correct explanation for this observation?

Electromagnetic spectrum

A student carries out an experiment to study double-slit interference with light, but the fringes formed on the screen are so close together that they cannot be told apart. Which change would make it easier for the student to distinguish the fringes?

Interference

Vessels have suffered damage from water waves of large amplitude. These waves may have been produced by the addition of the displacements of smaller waves. Which term is used for this phenomenon?

Interference

Water waves with wavelength $\lambda$ undergo diffraction when they travel through a barrier opening of width $d$. Which pairing of wavelength and gap width would give the largest diffraction angle?

Diffraction

Two horizontal parallel-plate conductors are spaced $20\ \text{mm}$ apart in air. The upper plate is earthed, and the lower plate has a potential of $+100\ \text{V}$. What is the electric field strength at point $P$ halfway between the plates?

Potential difference and power

When making reasonable estimates of physical quantities, which statement is incorrect?

Errors and uncertainties

Three metal plates of equal area are arranged in parallel. The gap between the top plate and the centre plate is $2.0\ \text{cm}$, while the distance from the centre plate to the bottom plate is $1.0\ \text{cm}$. The top plate is maintained at a potential of $+500\ \text{V}$, the middle plate at $+200\ \text{V}$ and the bottom plate is earthed, as shown. Determine the value of the ratio $\frac{\text{magnitude of force on an electron at } X}{\text{magnitude of force on an electron at } Y}$?

Potential difference and power

The diagram illustrates a graph. For a uniform metallic wire, what is the graph unable to represent?

Resistance and resistivity

An iron wire is $8.0\ \text{m}$ long and has a diameter of $0.50\ \text{mm}$. Its resistance is $R$. Another iron wire is $2.0\ \text{m}$ long and has a diameter of $1.0\ \text{mm}$. What is the resistance of this second wire?

Resistance and resistivity

The Atlantic torpedo is a sizable electric fish that can produce a voltage of $220\,\text{V}$ between its tail and its head. This creates a current pulse of $15\,\text{A}$ for a duration of $2.0\,\text{ms}$. The fish gives out $200$ pulses per second. Determine the average power output of the fish?

Potential difference and power

A thermistor and a second component are joined to a constant voltage supply. A voltmeter is placed across one of the components. The temperature of the thermistor is then lowered, while nothing else is altered. In which circuit does the voltmeter reading rise?

Potential dividers

As shown, a $110\,\text{V}$ d.c. supply is linked to a heater, a fuse and a switch. Because of a fault in the circuit, the heater does not receive power. A technician uses a voltmeter to find the fault. He then closes the switch and attaches his meter between the positive supply terminal $\text{S}^+$ and the fuse terminal $\text{F2}$. The voltmeter gives a reading of $110\,\text{V}$. Which diagnosis is the correct one?

Practical circuits

The diagram depicts a potentiometer and a fixed resistor joined across a $12\,\text{V}$ battery with negligible internal resistance. The fixed resistor and the potentiometer both have a resistance of $20\,\Omega$. The circuit is intended to give a variable output voltage. What is the range of output voltages?

Potential dividers

Radioactive decay happens unpredictably. What does the term random mean?

Atoms, nuclei and radiation

The nuclei of all isotopes of the same element each contain the same number of one particular particle. Which particle is this?

Atoms, nuclei and radiation

Which of the following statements about nuclei is correct?

Atoms, nuclei and radiation

A calibration graph is provided for an ammeter with an inaccurate scale. During an experiment, the meter gives two readings at different times: $0.13\,\text{mA}$ and $0.47\,\text{mA}$. What was the actual increase in current between these two readings?

Practical circuits

The diagram presents a section of a radioactive decay series in which the nuclide thorium-$232$ undergoes $\alpha$-emission to form radium-$228$. This nuclide is also unstable and undergoes $\beta$-emission to produce a nuclide of actinium. The sequence then proceeds further. $^{{232}}_{{90}}\text{Th} \xrightarrow{\alpha} ^{{228}}_{{88}}\text{Ra} \xrightarrow{\beta} ^{{X}}_{{89}}\text{Ac} \xrightarrow{Y} ^{{228}}_{{90}}\text{Th} \xrightarrow{\alpha} ^{{224}}\text{Z} \rightarrow$ What are $X$, $Y$ and $Z$?

Atoms, nuclei and radiation

Four identical rods each have a square cross-section. They are arranged side by side, and their total width is measured using vernier calipers, as shown. The reading is $(8.4 \pm 0.1)\,\text{mm}$ and the zero reading on the calipers is $(0.0 \pm 0.1)\,\text{mm}$. What is the width of a single rod?

Errors and uncertainties

A light-meter measures the intensity $I$ of the light falling on it. Theory predicts that $I$ varies inversely as the square of the distance $d$. Which graph of the results supports this theory?

Progressive waves

The following equation is one of the equations for uniformly accelerated motion. $s = ut + \frac{1}{2}at^2$ The apparatus is set up to measure the time $t$ for a marble to pass between two light gates linked to timers. Before being released, the marble is held against the stop. The vertical separation $s$ between the light gates is measured. Which graph does not represent the correct relationship when light gate 2 is raised towards light gate 1, which remains fixed?

Equations of motion

A stone is released from a height of $20\,\text{m}$ above water. The graph shows how the stone's velocity changes with time. Which statement describes the stone's approximate position four seconds after it is released?

Equations of motion

The water surface in a deep well lies $78.0\,\text{m}$ beneath the top of the well. From the top of the well, a person releases a heavy stone down the well. Air resistance is negligible. The speed of sound in air is $330\,\text{m s}^{-1}$. What is the time interval between the person releasing the stone and hearing it strike the water?

Equations of motion

Which list is arranged in order of increasing length from start to finish?

Physical quantities

A bus needs $25\,\text{s}$ to attain a constant speed as it moves in a straight line. A graph of speed $v$ against time $t$ is shown. Which graph shows how the resultant force $F$ on the bus varies with $t$?

Momentum and Newton's laws of motion

A single horizontal force $F$ acts on block X, which is touching a separate block Y, as shown. The blocks stay in contact while they accelerate along a horizontal frictionless surface. Air resistance is negligible. X has a greater mass than Y. Which statement is correct?

Momentum and Newton's laws of motion

A $0.20\,\text{kg}$ mass hangs from the lower end of a light spring. A further $0.10\,\text{kg}$ mass is attached to the first mass by a thread. The system is left to reach static equilibrium and then the thread is burnt through. At that moment, determine the upward acceleration of the $0.20\,\text{kg}$ mass. (Take $g = 10\,\text{m s}^{-2}$.)

Momentum and Newton's laws of motion

A body of mass $m$ moving at speed $v$ collides head-on with a second body of mass $m$ moving in the opposite direction at speed $v$. After the impact, the two bodies remain joined together. Determine the total loss of kinetic energy in this collision.

Linear momentum and its conservation

Two identical spheres X and Y move towards one another with the speeds shown and experience a head-on elastic collision. What are the velocities of the spheres after the collision?

Linear momentum and its conservation

Which pair of forces acts solely as a couple on the circular object?

Turning effects of forces

A car with mass $500\,\text{kg}$ is stationary at point X on a slope, as illustrated. The brakes are then released, and the car travels down the slope with the engine turned off. By the time it reaches point Y, it has descended a vertical height of $30\,\text{m}$ and its speed is $11\,\text{m s}^{-1}$. What amount of energy is dissipated by frictional forces as the car travels from X to Y?

Energy conservation

Under what circumstance is no work done?

Energy conservation

An electric railway locomotive produces a peak mechanical output power of $4.0\,\text{MW}$. It receives electrical power at $25\,\text{kV}$ through overhead wires. The locomotive’s overall efficiency in changing electrical power into mechanical power is $80\%$. What current is drawn from the overhead wires when the locomotive is running at maximum power?

Potential difference and power

The table gives a summary of some descriptions of evaporation. Which row in the table is the correct one?

Energy conservation

Which equation involves only scalar quantities?

Scalars and vectors

The diagram illustrates a cross-sectional view of an Olympic-size swimming pool containing water. The diagram is not to scale. The water has a density of $1000\,\text{kg m}^{-3}$. What is the pressure difference between X and Y?

Density and pressure

A force is applied to one wire, causing an extension $e$. That same force is then applied to a second wire made from the same material, but with half the diameter and three times the length of the first wire. Both wires obey Hooke’s law. What extension does the second wire experience?

Stress and strain

Which statement concerning elastic and plastic deformation is correct?

Elastic and plastic behaviour

What does the term ultimate tensile stress of a ductile metal mean?

Stress and strain

A $0.80\,\text{m}$ steel wire and a $1.4\,\text{m}$ brass wire are connected end to end. The joined wires hang from a fixed support, and a force of $40\,\text{N}$ is applied, as shown. The Young modulus of steel is $2.0 \times 10^{11}\,\text{Pa}$. The Young modulus of brass is $1.0 \times 10^{11}\,\text{Pa}$. Each wire has a cross-sectional area of $2.4 \times 10^{-6}\,\text{m}^2$. The wires stretch without reaching their elastic limits. Determine the total extension. Ignore the weights of the wires.

Stress and strain

Which of the following wave motions can be used to show the phenomenon of polarisation?

Polarisation

The figure depicts the display on a cathode-ray oscilloscope (c.r.o.) showing a wave. The time-base of the c.r.o. is adjusted to $10\,\text{ms/div}$. What is the frequency of this wave?

Progressive waves

P is a source that emits infra-red radiation, while Q is a source that emits ultra-violet radiation. The numbers in the table are proposed wavelengths for the radiation given off by P and Q. Which row is correct?

Electromagnetic spectrum

In the diagram, a tuning fork is positioned above an air column that has a length of $25\,\text{cm}$. A stationary wave forms in the tube at the same frequency as the tuning fork. The bottom of the tube is closed. This is the shortest tube length, with the bottom closed, that produces a stationary wave. Which other tube lengths, with their lower ends sealed, will also produce a stationary wave?

Stationary waves

White light is made up of many wavelengths. The wavelength of red light R is about twice that of violet light V. If white light is directed normally onto a diffraction grating, a number of spectra may be produced. Which diagram shows the possible arrangement of light in the first order and the second order spectra?

The diffraction grating

A satellite's orbital period $T$ for a circular orbit around the Earth is related by $T^2 = \frac{k r^3}{M}$, where $r$ is the radius of the orbit, $M$ is the mass of the Earth and $k$ is a constant. What are the SI base units of $k$?

SI units

For a stationary wave to be formed, two waves must move in opposite directions through the same region of space. Which statement about the characteristics of the two waves must also be correct?

Stationary waves

A potential difference is applied across two metal plates that are not parallel. Which diagram represents the electric field between the plates?

Potential difference and power

A particle located between two parallel metal plates has a charge of $8 \times 10^{-19}\,\text{C}$. The potential difference (p.d.) across the plates is $2000\,\text{V}$. The electric field exerts a force of $3.2 \times 10^{-13}\,\text{N}$ on the particle. What is the separation between the plates?

Potential difference and power

Which unit has the same magnitude as a coulomb (C)?

Electric current

The graph illustrates the $I$-$V$ characteristic of an electrical component. Which component is it?

Practical circuits

A power supply with electromotive force (e.m.f.) $12\,\text{V}$ and internal resistance $2\,\Omega$ is joined in series to a load resistor. The resistance of the load resistor is changed from $0.5\,\Omega$ to $4\,\Omega$. Which graph shows how the power $P$ dissipated in the load resistor changes with the resistance of the load resistor?

Potential difference and power

The diagram illustrates a resistor arrangement. What is the combined electrical resistance between X and Y?

Resistance and resistivity

A power supply has an electromotive force of $120\,\text{V}$. It provides a current of $1.2\,\text{A}$ to a resistor with resistance $80\,\Omega$ and a current of $0.40\,\text{A}$ to a second resistor, as illustrated. What is the internal resistance of the power supply?

Practical circuits

The diagram represents a four-terminal box linked to a battery and two ammeters. The readings on the two meters are the same. Which circuit inside the box would produce this outcome?

Kirchhoff's laws

A substance contains a radioactive isotope that decays only through the emission of $\alpha$-particles at a rate of $100\,\text{s}^{-1}$. Which statement about this substance is true?

Atoms, nuclei and radiation

Which row gives sensible estimates for the mass and the speed of an adult running?

Physical quantities

A radioactive nucleus emits an $\alpha$-particle or a $\beta$-particle, producing a product nucleus. Which decay process could have formed the product nucleus given?

Atoms, nuclei and radiation

A student records the period $T$ of one full swing of a pendulum with length $l$. Her measurements are listed in the table: $l / \text{m} = 0.420 \pm 0.001$ $T / \text{s} = 1.3 \pm 0.1$ She applies the equation $T = 2\pi \sqrt{\frac{l}{g}}$ to determine the acceleration of free fall $g$. What is the best estimate of the percentage uncertainty in the value of $g$?

Errors and uncertainties

In the diagram, two full pulses are displayed on the screen of a cathode-ray oscilloscope. The screen is overlaid with a grid made of $1\,\text{cm}$ squares. The time-base setting is $1\,\mu\text{s cm}^{-1}$. What is the duration of each pulse?

Practical circuits

A boy throws a ball straight up vertically. The ball climbs to a greatest height, where it is briefly stationary, and then comes back down into his hands. Which row shows the ball’s acceleration at each stage of its motion? (Treat vertically upwards as positive. Neglect air resistance.)

Equations of motion

The curved line PQR shows the velocity-time graph for a car that begins from rest. What is the car’s average acceleration during the first $5\,\text{s}$?

Equations of motion

A ball is let go from rest above a horizontal floor. It hits the floor and rebounds a number of times. The velocity-time graph for the first two rebounds is shown. What is the greatest height reached by the ball after the first bounce?

Equations of motion

In SI base units, which unit is used for the Young modulus?

Stress and strain

A football is let go above a plane, sloping surface and rebounds several times. The diagram illustrates its trajectory between the rebounds at $X$ and at $Y$. Assume that air resistance is absent. Which graph correctly shows how the horizontal component of its velocity $v_h$ varies with time $t$ between $X$ and $Y$?

Equations of motion

A rocket with mass $30\,000\,\text{kg}$ is resting on a launch pad at the Earth’s surface. The rocket motors exert an upward force of $330\,\text{kN}$ on the rocket. What is the rocket’s initial acceleration?

Momentum and Newton's laws of motion

Two equal masses X and Y are travelling towards one another on a frictionless air track, as shown. The masses undergo an elastic collision. Which row shows possible velocities of the two masses after the collision?

Linear momentum and its conservation

With reference to perfectly elastic collisions between two bodies, which statement is correct?

Linear momentum and its conservation

Which statement most accurately describes a couple?

Turning effects of forces

A cross-shaped arrangement, pivoted freely at O, has arms measuring $5.0\ \text{m}$, $4.0\ \text{m}$, $3.0\ \text{m}$ and $2.0\ \text{m}$. Forces of $2.0\ \text{N}$, $3.0\ \text{N}$, $4.0\ \text{N}$ and an unknown force $F$ act on it. The arrangement is in rotational equilibrium. What is the magnitude of force $F$?

Turning effects of forces

A trolley begins from rest at X. It moves down to Y and finally stops at Z. Which row could give a correct summary of the energy changes in this process?

Energy conservation

An object with weight $15.0\ \text{N}$ is drawn across a horizontal surface at a steady speed of $2.00\ \text{m s}^{-1}$. The pulling force on the object is $12.0\ \text{N}$ acting at $30^\circ$ to the horizontal, as shown. What is the power needed to move the object?

Energy conservation

Brownian motion may be shown by shining light on smoke particles in a sealed, transparent container. When the particles are examined with a microscope, bright points of light are seen to move in a continuous random manner. Which conclusion cannot be drawn from this observation?

Atoms, nuclei and radiation

One limb of a U-tube has a cross-sectional area of $A$, whereas the other limb has a cross-sectional area of $4A$. As illustrated, the tube is filled with water of density $1000\ \text{kg m}^{-3}$ and oil of density $850\ \text{kg m}^{-3}$. In the left-hand limb, the layer of oil resting above the water has a length of $30.0\ \text{cm}$. What is the height difference $x$ between the liquid levels in the two limbs of the tube?

Density and pressure

The Reynolds number $R$ is a constant employed in the analysis of liquids moving through pipes. $R$ is a dimensionless quantity, so it has no unit. $R = \frac{\rho v D}{\mu}$ where $\rho$ represents the density of the liquid, $v$ is the liquid's speed and $D$ is the diameter of the pipe in which the liquid flows. What are the SI base units of $\mu$?

SI units

The Young modulus of a metal can be found from the ratio $\frac{\text{stress}}{\text{strain}}$ while the metal is being stretched elastically. This may be carried out by taking readings as loads are applied to a wire. Which measurements are required in order to calculate the stress and strain in the wire for such an experiment?

Stress and strain

A copper wire that is $3.6\,\text{m}$ long and has diameter $1.22\,\text{mm}$ is stretched elastically by a force of $37\,\text{N}$. The Young modulus of copper is $1.17 \times 10^{11}\,\text{Pa}$. What extension does this force produce?

Stress and strain

When every other feature of a wave stays constant, which relationship is correct?

Progressive waves

A vibrating rod generates a water wave in a ripple tank. The graph shows the wave’s displacement at one particular moment as it moves away from the rod. The wave speed is $2.0\,\text{cm s}^{-1}$. What is the frequency of the wave?

Progressive waves

Polarisation is a phenomenon linked with a particular kind of wave. Which condition must be satisfied for a wave to be polarised?

Polarisation

Monochromatic light is sent through two narrow slits, forming an interference pattern on a screen some distance away. The interference fringes are very closely spaced. Which change would increase the spacing between the fringes?

Interference

The statements below describe the diffraction of waves as they travel through a narrow slit. Which statement is incorrect?

Diffraction

A beam of monochromatic light is shone at a pair of slits. On a screen far away, interference fringes spaced $2.0\,\text{mm}$ apart are seen. The frequency of the light is then doubled, and the separation of the slits is reduced to half. What is the spacing between the new interference fringes?

Interference

A diffraction grating contains $N$ lines per unit length and is set at $90^\circ$ to monochromatic light with wavelength $\lambda$. What expression gives $\theta$, the angle to the normal to the grating at which the third order diffraction peak is seen?

The diffraction grating

In a vacuum, two parallel plates R and S are separated by $2\,\text{mm}$. An electron, carrying charge $-1.6 \times 10^{-19}\,\text{C}$, travels in a straight line through the electric field between the plates. The graph illustrates how the electron’s potential energy changes with its distance from plate R. Which conclusion is incorrect?

Potential difference and power

If a force $F$ shifts its point of application by a displacement $s$ in the same direction as the force, the work $W$ done by the force is $W = Fs$. How many vector quantities, and how many scalar quantities, are present in this equation?

Scalars and vectors

Two parallel conducting plates, with air in the gap, are set very close to each other. The upper plate carries a negative charge and the lower plate is earthed. Which diagram shows the correct arrangement of charges and the electric field between the plates?

Potential difference and power

Using energy transfer $W$ and charge $q$, how are potential difference (p.d.) and electromotive force (e.m.f.) defined?

Potential difference and power

A cell with electromotive force $E$ and internal resistance $r$ is joined to an external resistor, as illustrated. The circuit current is $I$ and the potential difference (p.d.) across the external resistor is $V$. In the relationship $(E - V) = Ir$, what quantity is represented by $(E - V)$?

Practical circuits

Tensile strain can be determined from the variation in electrical resistance of a device known as a strain gauge. A strain gauge is made of a folded fine metal wire fixed onto a flexible insulating backing sheet. The strain gauge is attached securely to the specimen. As the strain in the specimen increases, what happens to the resistance of the wire?

Stress and strain

In the circuit diagram, lamp P has a rating of $250\,\text{V},\,50\,\text{W}$ and lamp Q has a rating of $250\,\text{V},\,200\,\text{W}$. These two lamps are joined in series to a $250\,\text{V}$ power supply. Assume that the resistance of each lamp stays constant. Which statement most accurately describes the situation when the switch is closed?

Potential difference and power

In many houses, the cooling system is managed by three electrical switches: a thermostat switch, which closes when the temperature reaches a specified value; a clock switch, which closes at times when cooling might be needed; and an override switch, which closes to switch on the system when unusually high temperatures occur. Which diagram shows these switches connected correctly between the power supply and the cooling system?

Practical circuits

A $110\,\text{V}$ supply with negligible internal resistance is linked to a heater via a fuse and a switch. The supply’s positive and negative terminals are $S^+$ and $S^-$. For fault-finding, points $C1$ and $C2$ on either side of the heater can be accessed. A voltmeter is placed between $S^-$ and $C1$. When the circuit operates correctly, the voltmeter reading is recorded while the switch is closed. A fault then develops, and the voltmeter is once more connected between $S^-$ and $C1$ with the switch still closed. Which fault would produce the same two voltmeter readings?

Practical circuits

An arrangement of resistors, each having resistance $1\,\Omega$, is joined as illustrated. The current in the resistor at the far end is $1\,\text{A}$. What is the potential difference (p.d.) $V$ between the input terminals?

Kirchhoff's laws

Two $\alpha$-particles with the same energies are directed towards the nucleus of a gold atom. Which diagram shows their paths most accurately?

Atoms, nuclei and radiation

When a nucleus emits an $\alpha$-particle, what changes occur in the proton number and the nucleon number of the nucleus before the emission?

Atoms, nuclei and radiation

Measurements may be affected by systematic error and random error. Which measurements show high accuracy but low precision?

Errors and uncertainties

A straightforward theory of $\alpha$-particle scattering from a thin metal foil is based on the four assumptions listed below. Which assumption is exact and is not an approximation?

Atoms, nuclei and radiation

The density of the material in a coil made from thin wire is to be determined. Which combination of instruments would allow this to be done most accurately?

Errors and uncertainties

A tube with a cylindrical shape rolls down a slope inclined at angle $\theta$ and travels a distance $L$ in a time $T$. The quantities are linked by $L\left(3 + \frac{a^2}{P}\right) = QT^2 \sin \theta$, where $a$ denotes the internal radius of the tube and $P$ and $Q$ are constants. Which row shows the correct units of $P$ and of $Q$?

Equations of motion

The variables $x$ and $y$ satisfy $y = p - qx$, with $p$ and $q$ as constants. Experimental measurements are taken for $x$ and $y$. The data include a systematic error. Which graph most accurately shows these results?

Errors and uncertainties

A cheetah and an antelope are $100\,\text{m}$ apart. After the cheetah sees the antelope, it runs towards it. The antelope responds to the cheetah after one second and moves straight away from the cheetah. It takes both animals $2\,\text{s}$ to attain their top speeds. The graph illustrates how the speeds of the two animals change with time. How far apart are the animals, $17\,\text{s}$ after the cheetah began running?

Non-uniform motion

A boy launches a stone horizontally at $10\,\text{m s}^{-1}$ from the roof of a building. The building is $8.0\,\text{m}$ high. The stone follows a curved trajectory before landing on the ground, as shown in the diagram. How long does it take the stone to reach the ground? (Air resistance can be neglected.)

Equations of motion