Oct/Nov 2023

What would be a sensible estimate for the cross-sectional area of the wire in a paper clip?

Physical quantities

Two objects travel directly towards one another along the same straight line. After they collide, the two objects remain attached and come to rest. Which statement has to be correct?

Linear momentum and its conservation

For a jar to be opened, a minimum torque of $20\,\text{N m}$ has to be exerted on its lid. The lid has a radius of $4.0\,\text{cm}$. What minimum force $F$ must be applied on each side of the lid so that it opens?

Turning effects of forces

A bar of uniform density, with length $L$ and weight $W$, is placed horizontally on two supports, $X$ and $Y$. At a point $rac{L}{6}$ from one end of the bar, support $X$ provides an upward force $R_X$. At the opposite end of the bar, support $Y$ provides an upward force $R_Y$. The bar is balanced in equilibrium. Determine the ratio $\frac{R_X}{R_Y}$?

Turning effects of forces

A firework of one kind is constructed by fixing two rockets to a rod, with the rockets pointing in opposite directions, as shown. The rod is mounted on a frictionless pivot, allowing the firework to turn in a vertical plane. The firework has weight $W$. The pivot applies a force $R$ to the rod that is equal in size and opposite in direction to $W$. Each rocket applies a force of magnitude $F$ to the rod at a perpendicular distance $d$ from the pivot. The directions of the forces produced by the rockets are always opposite. Air resistance is negligible. Which statement is correct?

Turning effects of forces

An object with weight $W$ is hung from a newton meter. When the object is fully immersed in water, the newton meter shows $P$. When the object is fully immersed in oil, the newton meter shows $Q$. What is the ratio $\dfrac{\text{density of oil}}{\text{density of water}}$?

Density and pressure

A crate with mass $50\,\text{kg}$ is moved $6.0\,\text{m}$ across a horizontal surface while a constant resistive force of $70\,\text{N}$ opposes the motion. The crate travels at constant speed. It is then raised, still at constant speed, through a vertical height of $1.2\,\text{m}$ onto the back of a lorry. What is the total work done in this process?

Gravitational potential energy and kinetic energy

The power supplied to a television is $P_{\text{in}}$. The useful sound and light power produced by the television is $P_{\text{out}}$. What is the efficiency of the television?

Energy conservation

A builder lets a brick of mass $3000\,\text{g}$ fall onto his foot. What is a sensible estimate of the change in gravitational potential energy of the brick?

Gravitational potential energy and kinetic energy

An elastic cord with an unstretched overall length of $16.0\,\text{cm}$ and a cross-sectional area of $2.0 \times 10^{-6}\,\text{m}^2$ is stretched horizontally between two smooth pins that are $8.0\,\text{cm}$ apart. The cord follows Hooke’s law. A load with mass $0.40\,\text{kg}$ is attached at the centre of the cord. The angle formed by the two sections of cord supporting the load is $60^{\circ}$. Determine the Young modulus of the cord material.

Stress and strain

Which force-extension graph indicates plastic deformation in a sample of material?

Elastic and plastic behaviour

Which quantity does not count as an SI base quantity?

SI units

Two waves travel through a point $P$. The graph illustrates how the displacement $s$ of the two waves at point $P$ changes with time $t$. What phase difference is there between the two waves at point $P$?

Progressive waves

For both progressive transverse waves and progressive longitudinal waves, which row is correct?

Progressive waves

A toy drone produces a sound with constant frequency $800\,\text{Hz}$. The speed of sound in air is $330\,\text{m s}^{-1}$. The drone travels in a straight line directly towards an observer and then carries on in the same straight line directly away from the observer. The drone moves at constant speed. Calculate the velocity of the drone when the frequency of the sound detected by the observer is $850\,\text{Hz}$?

Doppler effect for sound waves

Which statement concerning electromagnetic waves in a vacuum is correct?

Progressive waves

Microwaves that are vertically polarised are produced by a source. A receiver, linked to a cathode-ray oscilloscope (CRO), detects these microwaves. On the CRO screen, the displayed waveform has an amplitude of $2.6\,\text{cm}$. A metal wire grid acting as a polarising filter is then inserted between the source and the receiver. The filter is set so that the plane of polarisation of the transmitted wave makes an angle of $20^\circ$ with the vertical. The separation between the source and receiver stays the same. The CRO settings are also kept unchanged. What is the amplitude of the waveform now shown on the CRO screen?

Polarisation

During an experiment, a stationary wave is produced on a string stretched horizontally between two fixed points. Which statement about the experiment is correct?

Stationary waves

An organ creates notes by forcing air into a set of pipes, each of which is open at one end and closed at the other. The speed of sound in the air inside the pipes is $320\,\text{m s}^{-1}$. What is the lowest frequency of sound produced by a pipe of length $10\,\text{m}$?

Stationary waves

In an experiment, water waves in a ripple tank strike a gap, as shown. Some diffraction of the water waves is seen. Which change to the experiment would give a clearer demonstration of diffraction?

Diffraction

Light of wavelength $\lambda$ is produced by two point sources R and S and reaches a screen far away. The light intensity at point P on the screen is zero. What could account for the zero intensity at P?

Interference

A beam of red light with wavelength $720\,\text{nm}$ is directed normally onto a diffraction grating, creating a diffraction pattern on a screen that lies parallel to the grating. This red-light beam is then substituted by a beam of electromagnetic radiation with wavelength $X$, which also strikes the same diffraction grating at normal incidence. The third-order maximum for the radiation of wavelength $X$ appears at the same point on the screen as the second-order maximum for the red light. Determine wavelength $X$.

The diffraction grating

A student measures the acceleration of free fall by means of a small metal ball, as illustrated. When switch $S$ is turned on, the ball is released from an electromagnet and an electronic timer begins. The ball then drops straight down. The timer comes to a stop when the ball lands on a trapdoor. The student measures the distance $PQ$ between the electromagnet and the trapdoor. This distance, together with the timer reading, is then used to calculate the acceleration of free fall. Which statement about errors in the experiment is correct?

Errors and uncertainties

For a conductor, the current $I$ is described by the equation $I = Anvq$. In this equation, what does the symbol $n$ stand for?

Electric current

In the circuit diagram, the battery provides an electromotive force (e.m.f.) of $6.0\,\text{V}$ and has negligible internal resistance. Each of the three resistors has resistance $R$. The total power dissipated by the resistor network is $24\,\text{W}$. Determine the value of $R$.

Potential difference and power

Which graph might illustrate how the resistance $R$ of a filament lamp changes with the applied potential difference (p.d.) $V$, as $V$ is raised to the normal operating p.d.?

Resistance and resistivity

A piece of conducting putty has been formed into a cylinder with length $60\,\text{mm}$ and diameter $20\,\text{mm}$. The resistance measured between the two ends of the cylinder is $20\,\Omega$. What is the resistivity of the putty?

Resistance and resistivity

Which statement concerning the electromotive force (e.m.f.) of a cell is always true?

Potential difference and power

Kirchhoff’s first and second laws arise from the conservation of which quantities?

Kirchhoff's laws

A circuit includes a cell with electromotive force $E$ and internal resistance $r$, linked to a resistor with resistance $R$. The current in the circuit is $I$. Which equation is correct?

Practical circuits

A potential divider is made of two resistors with resistances $R_1$ and $R_2$ joined in series across a source of potential difference (p.d.) $V_{in}$. The p.d. measured across $R_1$ is $V_{out}$. Which changes to $R_1$ and $R_2$ would make $V_{out}$ larger?

Potential dividers

Two alpha-particles with equal kinetic energy are moving towards a gold nucleus and are then deflected by it. Which diagram might represent the paths taken by the two alpha-particles?

Atoms, nuclei and radiation

Which nuclide results when $^{10}_{6}\text{C}$ undergoes $\beta^{+}$ decay?

Atoms, nuclei and radiation

The diagram depicts two coplanar forces, $P$ and $Q$, shown to scale. Force $R$ is defined by $R = Q - P$. Which diagram shows $R$?

Scalars and vectors

A given hadron consists of three quarks and carries zero charge. What could be one possible quark composition for this hadron?

Fundamental particles

At time $t = 0$, a parachutist drops from a balloon that is initially stationary. The velocity-time graph for the parachutist from $t = 0$ up to the moment when he is just above the ground is shown. Which graph most accurately represents how the parachutist’s acceleration changes with time?

Equations of motion

A projectile is launched from point $P$ with velocity $V$ at an angle $\theta$ above the horizontal. It reaches point $Q$, which is a horizontal distance $R$ from $P$, after a time $T$. The acceleration of free fall is $g$. Air resistance can be ignored. Which equation is correct?

Equations of motion

A man is standing inside a lift that is accelerating downwards, as shown. Which statement best describes the force that the man exerts on the floor?

Momentum and Newton's laws of motion

A ball with mass $200\,\text{g}$ is projected horizontally at a speed of $20\,\text{m s}^{-1}$ towards a vertical wall. It remains in contact with the wall for $0.10\,\text{s}$ before bouncing back along the same line with a speed of $10\,\text{m s}^{-1}$. What is the average force exerted by the wall on the ball during the collision?

Momentum and Newton's laws of motion

A metal ball is released into a viscous liquid during an experiment. The ball’s terminal velocity in the liquid is then measured. The experiment is carried out four times. In each repeat, one of the following is altered. 1 the density of the metal of the ball 2 the height from which the ball is released 3 the density of the liquid 4 the depth of the liquid Which two changes, on their own, change the terminal velocity of the ball in the liquid?

Non-uniform motion

A student makes an estimate of the greatest speed for several different moving objects. Which greatest speed would not be a reasonable estimate?

Equations of motion

As illustrated, two balls of masses $m$ and $2m$ move through a vacuum with initial velocities $2v$ and $v$ respectively and collide head-on. After the impact, the ball with mass $m$ rebounds to the left at velocity $v$. What is the loss of kinetic energy in the collision?

Linear momentum and its conservation

A force $F$ acts on a door handle at a point $d$ from the handle’s pivot, making an angle of $45^\circ$ with the handle, as shown. What is the moment of the force about the pivot?

Turning effects of forces

A couple is formed by two forces, each of magnitude $F$, acting in opposite directions within the same plane. The perpendicular separation between the two forces is $d$. What is the torque of the couple?

Turning effects of forces

The diagram illustrates an experiment used to find the force acting on a ball due to a horizontal air flow. The ball hangs from a light string and has a weight of $0.15\,\text{N}$. The string is displaced $30^\circ$ from the vertical. The ball is in equilibrium. What is the force on the ball from the air flow?

Equilibrium of forces

As shown, two solid cylindrical objects X and Y are completely immersed in a liquid. Their volumes are equal. The density of the material of Y is twice the density of the material of X. Both objects are at rest. Which of the statements is correct?

Density and pressure

An electric car moves along a straight horizontal road at a steady speed of $70\,\text{km h}^{-1}$ over a distance of $80\,\text{km}$ and takes energy $E$ from its battery. The overall resistive force on the car is proportional to $(\text{speed})^2$. Assume that the electric motor is $100\%$ efficient. What amount of energy is taken from the battery when the car moves at a steady speed of $60\,\text{km h}^{-1}$ over the $80\,\text{km}$ straight horizontal road?

Energy conservation

What does the term efficiency of a system mean?

Energy conservation

When an object with mass $m$ is lifted by a vertical distance $\Delta h$, its gravitational potential energy increases by $\Delta E_p$. The quantities $\Delta E_p$ and $\Delta h$ are connected by $\Delta E_p = mg\Delta h$, where $g$ is the acceleration of free fall. The definition of which physical quantity is required to derive this equation?

Gravitational potential energy and kinetic energy

Three identical springs, all having the same spring constant, are joined together in four different arrangements, as shown. Which arrangement has the greatest overall spring constant?

Elastic and plastic behaviour

The force-extension graph for a wire is shown. Which row could correctly identify the labels X, Y and Z?

Elastic and plastic behaviour

Which quantity counts as an SI base quantity?

SI units

X and Y are two points on the water surface in a ripple tank. A source of constant frequency produces a wave that moves past X and Y, making them oscillate vertically. What is the phase difference between X and Y?

Progressive waves

A transverse wave travelling along a rope has wavelength $\lambda$ and period $T$. The graph illustrates how the displacement of the rope’s particles changes with distance in the direction of wave travel at time $t = 0$. Particle X is marked. Which graph shows how the displacement of particle X varies with time $t$?

Progressive waves

A source of sound waves is travelling at a steady speed straight towards a stationary observer. The sound waves move at $340\,\text{m s}^{-1}$ and have a frequency of $480\,\text{Hz}$. The observer detects sound waves with frequency $650\,\text{Hz}$. What is the speed of the source?

Doppler effect for sound waves

A student is studying two electromagnetic waves, X and Y, in a vacuum. Wave X has a wavelength of $5.2 \times 10^{-7}\,\text{m}$. Wave Y has a frequency of $9.4\,\text{GHz}$. Which main regions of the electromagnetic spectrum do waves X and Y belong to?

Electromagnetic spectrum

A plane-polarised light wave with intensity $I_0$ falls normally on a polarising filter. The intensity of the wave transmitted at first is $0$. A second polarising filter is then placed between the source and the first filter. Its transmission axis makes an angle of $45^\circ$ with the transmission axis of the first filter, as shown. What is the intensity of the wave transmitted by the filter combination?

Polarisation

What can describe the process by which stationary waves are produced from progressive waves?

Stationary waves

A pipe is $2.0\,\text{m}$ long. One end is open while the other end is closed. A stationary sound wave is established in the pipe. Within the pipe’s length, there are four nodes (N) and four antinodes (A). What is the wavelength of the sound wave?

Stationary waves

A teacher is describing diffraction to a class of students. Which piece of apparatus is the most suitable for the teacher to use to show diffraction?

Diffraction

Coherent light with a constant wavelength falls normally onto a double slit. Interference fringes appear on a screen positioned at a fixed distance from the double slit. The screen is parallel to the double slit. The slit separation is changed. Which graph best represents how the interference-fringe spacing $x$ varies with slit separation $a$?

Interference

Light of wavelength $690\,\text{nm}$ falls on a diffraction grating with 300 lines per mm, so a sequence of bright maxima is formed on a screen. How many bright spots are formed altogether?

The diffraction grating

A student records measurements in order to find the constant acceleration of a model car that starts from rest and travels in a straight line. The measured quantities, together with their absolute uncertainties, are listed below. Displacement: $16.5\,\text{m} \pm 0.1\,\text{m}$ Time: $15.0\,\text{s} \pm 1.0\,\text{s}$ To work out the car’s acceleration, the student applies the equation $s = \frac{1}{2}at^2$. What are the acceleration and its absolute uncertainty?

Errors and uncertainties

A very fine spray of oil droplets is released into the air. When the droplets pass out of the nozzle of the spraying device, they may acquire electric charge. What is not a possible value for the charge carried by an oil droplet?

Atoms, nuclei and radiation

In the circuit diagram, a fixed resistor $X$ is placed in series with a battery and a variable resistor. When a current of $3.0\,\text{A}$ flows through resistor $X$, the power dissipated in it is $7.2\,\text{W}$. The variable resistor is then changed so that the power dissipated in $X$ rises by $50\%$. What is the current in the circuit now?

Potential difference and power

The potential difference across a metal wire is held constant. The length $l$ and the diameter $d$ of the wire are both changed. The metal used stays the same. How does the current in the wire depend on $l$ and $d$?

Resistance and resistivity

A student assembles a circuit. The circuit diagram shows the way the positive terminal and negative terminal of a voltmeter are joined to the circuit. The voltmeter gives an initial positive reading. Which changes, if any, in temperature and light intensity would make the voltmeter reading fall?

Practical circuits

A battery with electromotive force (e.m.f.) $E$ and negligible internal resistance is connected in series with some resistors, as shown. Which statement is correct?

Potential dividers

Kirchhoff's first law follows from conservation of which physical quantity?

Kirchhoff's laws

The diagram represents a resistor network. Every resistor has a resistance of $6.0\,\Omega$. What is the total resistance of the network between points $X$ and $Y$?

Kirchhoff's laws

For the circuit diagram shown, a battery with negligible internal resistance is joined in series with two fixed resistors $R_1$ and $R_2$. This circuit will be used to check whether the electromotive force (e.m.f.) of a certain cell is $1.5\,\text{V}$. The cell is placed between terminals $X$ and $Y$, in parallel with $R_2$, and in series with a galvanometer. Which statement about this test is correct?

Potential dividers

Two nuclides are two isotopes of the same element. Which statement about the nuclides is correct?

Atoms, nuclei and radiation

The ratio of charge to mass, $r$, for a particle is defined by the equation below. $r = \frac{\text{charge on particle}}{\text{mass of particle}}$ The value of $r$ is found for an $\alpha$-particle, a $\beta^+$ particle and a proton $p$. Which list places the particles in order of increasing magnitude of $r$ from left to right?

Atoms, nuclei and radiation

A plane is travelling in a straight line at constant speed at an angle $\theta$ to the horizontal. The aeroplane experiences four forces: thrust force $T$, weight $W$, lift force $L$ and resistive force $R$. Which two equations must be true?

Equilibrium of forces

Which arrangement of up (u) and down (d) quarks makes up a neutron?

Fundamental particles

What does acceleration mean?

Equations of motion

An astronaut on the Moon, where air resistance is absent, throws a ball. The ball initially has a vertical velocity component of $8.00\,\text{m s}^{-1}$ and a horizontal velocity component of $4.00\,\text{m s}^{-1}$, as shown. The Moon’s acceleration of free fall is $1.62\,\text{m s}^{-2}$. What is the speed of the ball $9.00\,\text{s}$ after it is thrown?

Equations of motion

A $0.20\,\text{kg}$ block and a $0.50\,\text{kg}$ block are joined by a light inextensible string which runs over a frictionless pulley. At the start, the blocks are kept stationary. The $0.20\,\text{kg}$ block lies on a rough horizontal surface, whereas the $0.50\,\text{kg}$ block hangs freely in air. Air resistance is negligible. Once the blocks are released, their acceleration has magnitude $2.0\,\text{m s}^{-2}$. What is the magnitude of the frictional force between the $0.20\,\text{kg}$ block and the rough surface?

Momentum and Newton's laws of motion

A resultant force makes an object accelerate. What does the resultant force equal?

Momentum and Newton's laws of motion

An object is dropped from a helicopter that is stationary and eventually attains terminal velocity. What occurs to the object's acceleration from the moment it leaves the helicopter until it reaches terminal velocity?

Non-uniform motion

What is the most appropriate estimate of the wavelength of green light?

Electromagnetic spectrum

An object X, with mass $0.30\,\text{kg}$, is moving along a straight path with a constant velocity of $3.0\,\text{m s}^{-1}$ across a level surface with no friction. Object X then collides with a stationary object Y, which has mass $0.50\,\text{kg}$. Following the collision, X travels at $2.0\,\text{m s}^{-1}$ at an angle of $60^{\circ}$ to the direction in which it was moving before the collision. Object Y then moves with velocity $v$ at an angle of $41^{\circ}$ to the original direction of X, as illustrated. What is the value of $v$?

Linear momentum and its conservation

A uniform rigid beam with length $3.2\,\text{m}$ is supported on a pivot at its midpoint. As illustrated, two children are positioned at opposite ends of the beam. One child has mass $24\,\text{kg}$, while the other has mass $36\,\text{kg}$. Because the heavier child makes one end of the beam rest permanently on the ground, the beam is inclined at an angle of $20^{\circ}$ to the horizontal ground. Calculate the moment of the weight of the $24\,\text{kg}$ child about the pivot.

Turning effects of forces

A sailing boat has a mast and a boom as two of its parts. The mast is a vertical rigid beam, while the boom is a horizontal rigid beam. One end of the boom is joined to the mast with a pivot. The opposite end of the boom is linked to the mast by a rope, as shown. The rope makes an angle of $40^{\circ}$ to the horizontal and applies a tension force $T$ on the boom. The boom has a weight of $200\,\text{N}$. Its mass is evenly spread along its length. The boom is in equilibrium. What is the magnitude of $T$?

Turning effects of forces

Full-fat milk consists of fat-free milk combined with fat. A volume of $1.000 \times 10^{-3}\,\text{m}^3$ of full-fat milk has a mass of $1.035\,\text{kg}$. By volume, it is $4.00\%$ fat. The density of fat-free milk is $1.040 \times 10^{3}\,\text{kg m}^{-3}$. Determine the density of fat.

Density and pressure

Which formula for pressure is the correct one?

Density and pressure

A wooden cylinder is floating in water, with part of it below the surface. A force $F$ is exerted on the cylinder until it becomes just fully submerged. Which statement is not correct?

Density and pressure

A system has a useful power output of $4.0\,\text{W}$ and a wasted power of $16\,\text{W}$. Determine the efficiency of the system.

Energy conservation

A parachutist is moving down towards the ground with constant speed $v$. The rate at which her gravitational potential energy decreases is $R$. The acceleration of free fall is $g$. What is the mass of the parachutist?

Gravitational potential energy and kinetic energy

A copper wire whose diameter is $1.6\,\text{mm}$ is extended, while remaining within its limit of proportionality, by a tensile force of $430\,\text{N}$. The Young modulus of copper is $130\,\text{GPa}$. Determine the strain in the wire.

Stress and strain

Compressive forces act normally on the end faces of a cylinder with initial length $L$. The forces shorten the cylinder so that its length becomes $0.6L$. Once the compressive forces are removed, the cylinder’s length increases to $0.8L$. What describes the deformation of the cylinder when its length was $0.6L$?

Elastic and plastic behaviour

In an electric circuit, an ammeter shows $2\,\mu\text{A}$. In a second circuit, the ammeter shows $1\,\text{mA}$. By what factor is the current in the second circuit greater than the current in the first circuit?

Electric current

As sound passes through air, the air particles oscillate. A graph of displacement versus time for one air particle is shown. Which graph indicates how the kinetic energy of the air particle changes with time?

Progressive waves

A wave is moving across the surface of water. P, Q, R and S are four water particles on the surface. The diagram shows where the particles are at one particular moment. The wave is travelling from left to right. Which two particles are just about to move upwards?

Progressive waves

A loudspeaker produces sound with frequency $f_s$. The loudspeaker is fitted to a car that travels straight towards a stationary observer and its speed is increasing. Which statement gives the frequency of the sound heard by the observer?

Doppler effect for sound waves

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

Electromagnetic spectrum

A vertically polarised electromagnetic wave with intensity $I_0$ is incident normally on a polarising filter. The filter’s transmission axis makes an angle of $30^\circ$ to the vertical. The wave that emerges from the first filter then falls normally on a second polarising filter. The transmission axis of this filter makes an angle of $90^\circ$ to the vertical. What is the intensity of the wave after it has passed through the second filter?

Polarisation

Which statement about a stationary wave is correct?

Stationary waves

Stationary sound waves may be produced in the air columns inside pipes. One kind of pipe has one end closed and the other end open. A different kind of pipe has both ends open. Which pipe is able to produce a stationary sound wave with the lowest frequency?

Stationary waves

Water waves in a ripple tank are sent through a narrow opening, as shown. Which diagram shows the waves after they have gone through the opening?

Diffraction

Light from a single wavelength falls normally on a double slit. The slit separation may be changed. A screen is positioned at a fixed distance from the double slit, and the screen is parallel to it. A pattern of bright interference fringes is seen on the screen. Which graph shows best how the spacing $x$ of the bright interference fringes varies with the slit separation $a$?

Interference

A diffraction grating is being used to determine the wavelength of light. The slit separation in the grating is $1.15 \times 10^{-6}\,\text{m}$. The angle between the first-order diffraction maxima is $60.0^{\circ}$, as shown. What is the wavelength of the light?

The diffraction grating

Repeated readings are taken of a constant quantity. Their mean is then found. What effect does taking the mean have on the random error and the systematic error in the readings?

Errors and uncertainties

What could not be used to generate an electric current?

Electric current

What does the term potential difference (p.d.) across a component mean?

Potential difference and power

As the current through a filament lamp rises, its resistance also rises. Why does this happen?

Resistance and resistivity

A battery with an electromotive force (e.m.f.) $12\,\text{V}$ and negligible internal resistance is joined to a fixed resistor of resistance $40\,\Omega$ and a thermistor of resistance $R_T$, as illustrated. At first, the thermistor is at a temperature of $15^{\circ}\text{C}$, and the current in the circuit is $0.10\,\text{A}$. The thermistor is then heated or cooled, causing the current to rise to $0.12\,\text{A}$. State how the temperature of the thermistor changes and determine $R_T$ at the new temperature.

Resistance and resistivity

A cell with electromotive force (e.m.f.) $3.0\,\text{V}$ and internal resistance $0.50\,\Omega$ is joined to a variable resistor, a voltmeter and an ammeter, as shown. The resistance of the variable resistor is changed. The ammeter reading $I$ and the voltmeter reading $V$ are noted. Which graph shows the way $V$ changes with $I$?

Potential difference and power

Three resistors, $R_1$, $R_2$ and $R_3$, are joined in parallel to a cell. The currents through the resistors are $I_1$, $I_2$ and $I_3$. The p.d.s across the resistors are $V_1$, $V_2$ and $V_3$. The current in the cell is $I_0$. The p.d. across the cell is $V_0$, as shown. Which equation can be deduced by applying Kirchhoff's second law to the circuit?

Kirchhoff's laws

A network contains three resistors, and each resistor has resistance $R$, as illustrated. The combined resistance between points X and Y is $8.0\,\Omega$. What is the value of $R$?

Resistance and resistivity

A potentiometer together with a driver cell of electromotive force (e.m.f.) $E$ is used to determine the e.m.f. of a new cell. The sliding contact at $P$ is adjusted along the resistance wire $QR$ until the galvanometer shows zero deflection. What condition must be satisfied for the e.m.f. of the new cell to be measured with accuracy?

Practical circuits

The table lists the number of nucleons and the overall count of particles (protons, neutrons and electrons) in neutral atoms of four nuclides $W$, $X$, $Y$ and $Z$. Which two nuclides are isotopes of one another?

Atoms, nuclei and radiation

If a sample of a radioactive isotope decays through $\alpha$-particle emission, the $\alpha$-particles produced all possess one fixed, discrete energy. If a sample of a radioactive isotope decays through $\beta$-particle emission, the $\beta^{-}$ particles produced have energies spread continuously over a range. What accounts for this difference?

Atoms, nuclei and radiation

A boat travels across a river whose water flows from left to right at $4.0\,\text{m s}^{-1}$. In still water, the boat has a speed of $6.0\,\text{m s}^{-1}$. The boat is aimed at an angle $\theta$ to a line that is perpendicular to the river banks. The combined velocity $v$ of the boat points in a direction perpendicular to the river banks. Determine the values of $\theta$ and $v$.

Scalars and vectors

Certain particles consist of three quarks combined together. Which set of quarks does not give a particle with a charge of either $+1.6 \times 10^{-19}\,\text{C}$ or zero?

Fundamental particles

A student travels at a steady speed over a distance of $50\,\text{m}$ in $40\,\text{s}$. The student then stops and rests for $10\,\text{s}$ before returning to the starting point at a steady speed in $30\,\text{s}$. What is the distance-time graph for the student’s motion?

Equations of motion

For an object released from rest and falling through a given distance on Mars, the time taken is $T_M$. For the same object, released from rest and falling through that same distance on Earth, the time taken is $T_E$. The acceleration of free fall on Mars is $3.71\,\text{m s}^{-2}$. Air resistance may be taken as negligible on both Earth and Mars. What is the ratio $\frac{T_M}{T_E}$?

Equations of motion

Which statement concerning mass is correct?

Physical quantities

A snooker ball has a mass of $200\,\text{g}$. It collides with the cushion on a snooker table and rebounds along its original line of motion. The ball reaches the cushion at $14.0\,\text{m s}^{-1}$ and then moves away at $7.0\,\text{m s}^{-1}$. The contact time between the ball and the cushion is $0.60\,\text{s}$. What is the average force exerted on the ball by the cushion?

Momentum and Newton's laws of motion

A ball is released from rest and falls through air until it eventually attains a constant velocity. During this motion, forces X and Y change with time as shown. What could forces X and Y be?

Momentum and Newton's laws of motion