Oct/Nov 2022

What must be used to represent all physical quantities accurately?

Physical quantities

Two trolleys are kept in contact on a horizontal surface, with a compressed spring placed between them. Once they are released, the trolleys separate from the spring. The trolley with mass $2\,\text{kg}$ travels to the left with a final speed of $2\,\text{m s}^{-1}$. What amount of elastic potential energy was stored in the spring?

Energy conservation

A square board with side length $x$ is suspended freely from a nail P, as illustrated. The board is of uniform thickness and is made from material with uniform density. Another square board, with side length $2x$, is made from the same material and has the same thickness as the first board. This second board is then suspended from a nail Q. Nails P and Q are level with each other. What is the vertical distance between the positions of the centres of gravity of the two boards?

Turning effects of forces

A rigid object is acted on by forces. All the forces lie in the same plane. In which diagram is the object in equilibrium?

Equilibrium of forces

A rigid rod XY, of negligible mass, is $75\,\text{cm}$ long. It is hung from a fixed point P using a string fixed to end X. A mass of $11\,\text{kg}$ is hung by a string attached to the rod $25\,\text{cm}$ from end X, as illustrated. What vertically upward force applied at end Y of the rod would keep the rod in horizontal equilibrium?

Turning effects of forces

The density of water is $1.0\,\text{g cm}^{-3}$, whereas the density of glycerine is $1.3\,\text{g cm}^{-3}$. Water is poured into a measuring cylinder that already contains $40\,\text{cm}^3$ of glycerine until the density of the mixture becomes $1.1\,\text{g cm}^{-3}$. Assume that mixing does not alter the total volume of the liquid. What volume of water is added?

Density and pressure

A cube-shaped box drops from a ship into the sea. It reaches the water with its bottom face exactly level with the sea surface. The box starts to sink, is then completely underwater, and afterwards continues to move further down into the sea. While the box is descending, its bottom face remains parallel to the sea surface at all times. Which graph shows best how the upthrust on the box changes with the depth of its bottom face below the sea surface?

Density and pressure

A mass compresses a spring, as illustrated. Which statement explains how the spring’s energy changes as it is compressed by the mass?

Energy conservation

A man with a mass of $75\,\text{kg}$ runs up a staircase made up of $30$ steps. Each step has a height of $20\,\text{cm}$. He takes $7.0\,\text{s}$ to run from the bottom of the staircase to the top. What is the average rate of increase in the man's gravitational potential energy?

Gravitational potential energy and kinetic energy

An alpha-particle possesses $2.2 \times 10^{-13}\,\text{J}$ of kinetic energy. What is the speed of the alpha-particle?

Atoms, nuclei and radiation

Four arrangements are made using identical springs. Which arrangement has the same spring constant as one spring?

Stress and strain

A voltmeter connected across a resistor in a circuit gives a reading of $3.6\,\text{V}$. Which set of values could represent the current in the resistor and the resistance of the resistor?

Resistance and resistivity

A spring that has not been extended measures $2.0\,\text{cm}$ in length. It is then pulled, but only up to its limit of proportionality, by a tensile force of $1.5\,\text{N}$. The elastic potential energy stored in the spring becomes $0.045\,\text{J}$. Determine the spring’s length when stretched.

Elastic and plastic behaviour

A signal generator, amplifier and loudspeaker are used to create different sound waves in the air within a room. The links between the properties of these waves are examined. Which relationship is incorrect?

Progressive waves

When a guitar string is plucked, it produces a longitudinal sound wave in the air, as illustrated. In air, the speed of sound is $340\,\text{m s}^{-1}$. What is the approximate frequency of the wave shown?

Progressive waves

A transverse wave is moving along a rope. The diagram shows the rope at time $t = 0$. The wave is moving from left to right. Its period is $T$. A particle on the rope is marked $X$. Which graph shows how the displacement of particle $X$ varies with time from $t = 0$ to $t = 2T$?

Transverse and longitudinal waves

A jet aircraft moves at a speed of $0.80v$, where $v$ represents the speed of sound. The aircraft is heading straight towards a stationary observer. The sound produced by the aircraft has a frequency of $100\,\text{Hz}$. What frequency is heard by the observer?

Doppler effect for sound waves

A telescope is used to detect and analyse electromagnetic radiation with wavelength $2\,\text{cm}$. What type of telescope is it?

Electromagnetic spectrum

Two waves of the same kind overlap. Under what conditions does the principle of superposition apply?

Progressive waves

A stationary sound wave is set up in a tube of length $L$ with one end closed. The diagram indicates the node and antinode positions of the stationary wave. Which graph shows how the amplitude $a$ of the wave changes with distance $x$ measured from the closed end of the tube?

Stationary waves

A surface water wave travels through a gap between two barriers and is diffracted, as shown. What happens when the wave frequency is halved?

Diffraction

Visible interference fringes are formed with light passing through a double slit. At first, the light coming out of each slit has the same intensity. The intensity of the light coming out of one slit is then decreased. How does this affect the interference pattern?

Interference

To find the acceleration of free fall $g$, an experiment measures the time $t$ for a ball to drop a distance $s$. The percentage uncertainty in measuring $s$ is $2\%$. The percentage uncertainty in measuring $t$ is $3\%$. The value of $g$ is found from the equation below. $g = \frac{2s}{t^2}$ What is the percentage uncertainty in the value of $g$ that is calculated?

Errors and uncertainties

A diffraction grating contains $4.00 \times 10^5$ lines per metre. Light with wavelength $589 \times 10^{-9}\,\text{m}$ falls normally on the diffraction grating. What is the angle between the second-order maximum and the line of travel of the incident beam of light?

The diffraction grating

The wire RS has a circular cross-section along its length. At the R end of the wire, the cross-sectional area is $A$. At the S end of the wire, the cross-sectional area is $\frac{A}{2}$. A charge of $Q$ requires time $t$ to move through the R end of the wire. The current in the wire is constant. What amount of charge will pass through the S end in a time interval of $\frac{t}{4}$?

Electric current

A power supply is linked to a component by connecting wires whose total resistance is $4.9\,\Omega$. The power supply delivers an output power of $3.6\,\text{W}$ and has a terminal potential difference of $12\,\text{V}$. Calculate the amount of thermal energy dissipated in the connecting wires during a time of $1.0$ hour?

Potential difference and power

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

Resistance and resistivity

Three identical filament lamps, P, Q and R, are connected to a battery with negligible internal resistance, as shown. The filament in lamp Q breaks, so that it no longer carries current. What changes occur in the brightness of lamps P and R?

Practical circuits

Which ratio is measured in the same units as electromotive force (e.m.f.)?

Potential difference and power

A circuit contains a battery, a voltmeter and five fixed resistors, as illustrated. The voltmeter shows a reading of zero. What is the resistance of resistor $R$?

Potential dividers

A battery with an electromotive force (e.m.f.) of $6.0\,\text{V}$ and negligible internal resistance is joined to a voltmeter and four other components, as shown. The voltmeter is placed across points X and Y. Its positive terminal is linked to X, while its negative terminal is linked to Y. At the start, the resistance of each of the four components is $1.0\,\text{k}\Omega$. Which single change will make the voltmeter give a positive reading?

Practical circuits

When an $b1$-particle moves very near to a gold nucleus, it is deflected by an angle above $90^
e$. Which property of the $b1$-particle is changed by this deflection?

Momentum and Newton's laws of motion

A nucleus of $^{238}_{92}c6$ undergoes a sequence of decays by releasing $b1$-particles and $b2^-$ particles, and finally becomes a nucleus of $^{206}_{82}43$. How many $b1$-particles and how many $b2^-$ particles are released in the decay chain?

Atoms, nuclei and radiation

Which one of the quantities is a vector?

Scalars and vectors

Which list of particles includes only fundamental particles?

Fundamental particles

A particle begins at rest. The graph illustrates how the particle’s velocity $v$ changes with time $t$. Which graph shows how the velocity $v$ changes with the acceleration $a$ of the particle?

Equations of motion

The graph illustrates the parachutist’s vertical velocity during the first $20\,\text{s}$ of her jump. Approximately how far does she descend before the parachute opens?

Non-uniform motion

How is linear momentum defined?

Momentum and Newton's laws of motion

A $0.20\,\text{kg}$ mass hangs from the lower end of a light spring. A $0.10\,\text{kg}$ mass is then attached to this first mass by a thread. The system is left to reach static equilibrium, and then the thread is severed. At the instant just after the thread is severed, what upward acceleration does the $0.20\,\text{kg}$ mass have?

Momentum and Newton's laws of motion

A snowflake and a raindrop are suspended in still air. They begin to fall from rest at the same instant and from the same height, which is far above the ground. The snowflake and the raindrop each contain the same mass of water. Assume that neither evaporation nor melting takes place. Also assume that, at any given speed, the drag force on the snowflake is larger than the drag force on the raindrop. Which statement about the snowflake and the raindrop is correct?

Non-uniform motion

Which of the following quantities is a physical quantity?

Physical quantities

A parachutist starts from rest while dropping from a balloon. The graph shows how the parachutist’s vertical velocity varies with time. In which region is the air resistance force much greater than the parachutist’s weight?

Non-uniform motion

Two solid spheres make up an isolated system. Sphere X is travelling in a straight line at a speed of $6\,\text{cm s}^{-1}$ directly towards a sphere Y that is at rest, as illustrated. The collision between the spheres is perfectly elastic. Once the collision is over, sphere X continues in the same direction as before, but now at a speed of $2\,\text{cm s}^{-1}$. What is the speed of sphere Y?

Linear momentum and its conservation

Which condition is not required for the forces in a couple?

Turning effects of forces

A box with length $12\,\text{cm}$ and weight $0.43\,\text{N}$ rests on a horizontal table, with most of its length projecting beyond the table edge. The table edge serves as the pivot. The box's centre of gravity is located at its geometric centre. In order to keep the box balanced, a uniform sphere of diameter $2.4\,\text{cm}$ is placed inside the box so that it touches one end, as illustrated. Take the forces on the box to lie in the plane of the diagram. What is the minimum mass of the sphere required to keep the system in equilibrium?

Turning effects of forces

A single object hangs from two ropes. One of the ropes exerts a tension of $410\,\text{N}$ and makes an angle of $60^\circ$ with the horizontal. The other rope exerts a tension of $210\,\text{N}$ and makes an angle of $10^\circ$ with the horizontal. The object is balanced. What is the mass of the object?

Equilibrium of forces

A solid cube is in equilibrium while floating in liquid mercury. It is made of iron with density $7900\,\text{kg m}^{-3}$. The cube floats with $42\%$ of its volume above the mercury surface. What is the density of the mercury?

Density and pressure

The diagram depicts two vessels, P and Q, each with sides inclined at $45^\circ$ to the horizontal. Vessel P widens towards the top, while vessel Q narrows towards the top, as shown. Both vessels hold a liquid. The liquid depth is the same in each vessel. The liquid in vessel P is twice as dense as the liquid in vessel Q. What is the ratio pressure from the liquid on the base of P : pressure from the liquid on the base of Q?

Density and pressure

A motor is employed to raise a load straight upwards. The load has weight $W$. The motor gives a useful power output $P$. The load moves upwards at constant velocity $v$. Which expression shows the time needed for the motor to lift the load vertically upwards by a distance $d$?

Gravitational potential energy and kinetic energy

A lamp is left on for $2.0$ hours. Its power input is $1.0\,\text{W}$. The energy released by the lamp as light is $7.0 \times 10^3\,\text{J}$. How much energy is changed into other forms by the lamp?

Energy conservation

An object with mass $m$ is released from rest onto the surfaces of two planets, X and Y, both of which have no atmosphere. The drop height and the resulting change in the object’s gravitational potential energy are listed for each planet in the table. For planet X: drop height $3\,\text{m}$, change in gravitational potential energy $\Delta E$. For planet Y: drop height $4\,\text{m}$, change in gravitational potential energy $4\Delta E$. The acceleration of free fall close to the surface of planet X is $g_x$. What is the acceleration of free fall close to the surface of planet Y?

Gravitational potential energy and kinetic energy

What is $3.7\,\text{MW}$ equal to in kilowatts?

SI units

A metal wire is subjected to a known tensile force. The wire remains below its limit of proportionality. Which two measurements are needed to calculate the strain in the wire?

Stress and strain

Different forces are used to stretch a wire. The wire follows Hooke’s law. A graph is drawn to show how a quantity $y$ changes with a quantity $x$. What might $x$ and $y$ be?

Elastic and plastic behaviour

A wave pulse travels along a stretched rope in the direction indicated. Which diagram shows how the displacement $s$ of particle $P$ in the rope varies with time $t$?

Progressive waves

Which statement about progressive transverse and longitudinal waves is correct?

Transverse and longitudinal waves

A miniature loudspeaker, starting from rest, drops vertically from a window in a tall building. After it has fallen a distance of $10.0\,\text{m}$, it emits a very brief sound pulse with constant frequency $256\,\text{Hz}$ in all directions. The sound pulse, moving at a speed of $330\,\text{m s}^{-1}$, is detected by a person leaning out of the window. Air resistance is negligible. What frequency is heard by the person for the sound pulse?

Doppler effect for sound waves

Two electromagnetic waves possess wavelengths of $5.0 \times 10^{-7}\,\text{m}$ and $5.0 \times 10^{-2}\,\text{m}$ in a vacuum. Which row names the regions of the electromagnetic spectrum that the waves are part of?

Electromagnetic spectrum

The wavelength of sound in air can be found by making use of stationary waves. In one investigation, a loudspeaker emits a sound wave of fixed frequency, and a metal plate about $1\,\text{m}$ away reflects it straight back along the same route. A microphone linked to a cathode-ray oscilloscope (CRO) is then shifted between the loudspeaker and the plate to locate positions of maximum sound intensity ('loud' spots) and minimum sound intensity ('quiet' spots). The sound wavelength is calculated using the smallest possible number of measured quantities. Which row gives the quantities that are required?

Stationary waves

Two progressive waves arrive at a stationary point $P$. The graph shows how the displacement of each wave at point $P$ changes with time. The two waves overlap at point $P$. What is the resultant displacement at time $0.38\,\text{s}$?

Progressive waves

Under what situation does diffraction take place?

Diffraction

Monochromatic light is directed at two very narrow slits separated by a distance of $0.10\,\text{mm}$. On a screen $2.0\,\text{m}$ away, an alternating pattern of bright and dark fringes is formed. The spacing between neighbouring bright fringes is $8.0\,\text{mm}$. What path difference between the waves from the two slits corresponds to the second-order dark fringe?

Interference

A spring is hung from a fixed support, and a force is then exerted on it. The reading of a pointer attached to the lower end of the spring is noted using a vertical ruler. Before any force is exerted, the pointer reads $(225 \pm 2)\,\text{mm}$. Once the force has been exerted, the pointer reads $(250 \pm 2)\,\text{mm}$. The spring’s extension is found. What is the percentage uncertainty in the extension?

Errors and uncertainties

Red light with one wavelength is sent through a diffraction grating. Bright spots appear on a screen, as shown. The red light is then changed to white light. Which diagram, drawn to the same scale, could show a possible pattern of bright light on the screen?

The diffraction grating

A nichrome wire has a resistance of $15\,\Omega$ and a diameter measuring $3.0\,\text{mm}$. The free-electron number density in nichrome is $9.0 \times 10^{28}\,\text{m}^{-3}$. A potential difference (p.d.) of $6.0\,\text{V}$ is applied across the two ends of the wire. What is the mean drift speed of the free electrons in the wire?

Electric current

The diagrams display two different circuits. In each circuit, the cells have the same electromotive force (e.m.f.) and negligible internal resistance. Each of the three resistors has resistance $R$. In the circuit on the left, the power dissipated in the resistor is $P$. What is the total power dissipated in the circuit on the right?

Potential difference and power

The potential difference (p.d.) across a filament lamp is raised. Which statement is correct?

Resistance and resistivity

A metal wire has resistance $R$. It is stretched until its diameter falls to $94.0\%$ of its initial diameter. The wire’s volume remains unchanged. What is the resistance of the stretched wire?

Resistance and resistivity

The diagram shows a cell with electromotive force (e.m.f.) $3.0\,\text{V}$ and internal resistance $4.7\,\Omega$ connected across a lamp. The lamp has a resistance of $9.3\,\Omega$. What is the power dissipated by the internal resistance of the cell?

Practical circuits

The circuit shown includes a battery, a high-resistance voltmeter and four fixed resistors. The battery provides an electromotive force (e.m.f.) of $15.0\,\text{V}$ and has negligible internal resistance. What value is indicated by the voltmeter?

Practical circuits

A potential divider circuit is intended to sense the temperature difference between two separate locations. The cell has an electromotive force (e.m.f.) of $20\,\text{mV}$ and negligible internal resistance. At the start, thermistors $X$ and $Y$ are at the same temperature and therefore have equal resistance. The voltmeter shows $10\,\text{mV}$. $X$ is then moved into a cold environment, so its resistance becomes twice its original value. $Y$ is then moved into a warm environment, so its resistance falls to half its original value. What is the voltmeter reading now?

Potential dividers

In the $\alpha$-particle scattering experiment, a beam of $\alpha$-particles is directed at a thin gold foil. The majority of the $\alpha$-particles pass straight through or are turned through a small angle. Only a very small number are scattered by more than $90^\circ$, so that they appear to bounce back towards the source of the $\alpha$-particles. From this experiment alone, which conclusion about atomic structure cannot be made?

Atoms, nuclei and radiation

Which pair of particles have charges of opposite sign?

Atoms, nuclei and radiation

How does a scalar quantity differ from a vector quantity?

Scalars and vectors

Which particle counts as a lepton?

Fundamental particles

A model toy car moves round a circular track with a steady speed of $0.50\,\text{m s}^{-1}$. It crosses a marked point on the track at time $t = 0$ and needs $40\,\text{s}$ to complete one full lap. The size of the average velocity of the car from $t = 0$ to $t = 20\,\text{s}$ is $v_{20}$. The size of the average velocity of the car from $t = 0$ to $t = 40\,\text{s}$ is $v_{40}$. What are $v_{20}$ and $v_{40}$?

Scalars and vectors

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

Non-uniform motion

At time $t = 0$, a goods train is moving through a station at a constant speed of $10\,\text{m s}^{-1}$. An express train is stationary at the station. The instant the goods train passes, the express train sets off from the station with a uniform acceleration of $0.5\,\text{m s}^{-2}$. The two trains travel in the same direction on straight, parallel tracks. For what value of $t$ does the express train catch up with the goods train?

Equations of motion

A constant resultant force $F$ is applied to an object of mass $m$ for a time $t$. What is the object’s change in momentum?

Momentum and Newton's laws of motion

The acceleration of free fall at the surface of planet P is one-tenth of the acceleration of free fall at the surface of planet Q. At the surface of P, an object has a mass of $1.0\,\text{kg}$ and a weight of $1.0\,\text{N}$. What are the mass and the weight of this same object at the surface of planet Q?

Momentum and Newton's laws of motion

A train having a mass of $600\,000\,\text{kg}$ travels at a speed of $100\,\text{km h}^{-1}$. What is the order of magnitude of the train’s kinetic energy?

Gravitational potential energy and kinetic energy

Two blocks are initially stationary on a frictionless horizontal surface. One is wooden and the other is steel. A steel ball is launched horizontally at speed $v$ towards the wooden block. The ball becomes embedded in the block, so after the impact the ball and block travel together. A second identical steel ball is launched horizontally at speed $v$ towards the steel block. This steel ball then bounces back along its original line of motion with speed $\frac{v}{2}$. The wooden block and the steel block have the same mass. Which statement about the blocks immediately after the collisions is correct?

Linear momentum and its conservation

Which diagram illustrates a couple produced by two forces, each with magnitude $F$, acting on a rod?

Turning effects of forces

A student claims that: If an object is in equilibrium, the total clockwise moment about a point $X$ is the same as the total anticlockwise moment about a point $Y$. Which condition would need to be true for the student’s statement to be correct?

Turning effects of forces

A rod of uniform composition with a length of $30\,\text{cm}$ and a weight of $5.2\,\text{N}$ is fixed to a wall by a hinge at one end. Its far end is held up by a wire, so that the rod stays horizontal and in equilibrium. The wire makes an angle of $40^\circ$ to the horizontal. Calculate the tension in the wire.

Turning effects of forces

Water is forced through a nozzle at the end of a hose. The nozzle has a circular cross-section with diameter $50\,\text{mm}$. A mass of $100\,\text{kg}$ of water takes $2.0\,\text{s}$ to pass through the nozzle. The density of water is $1000\,\text{kg m}^{-3}$. What is the water speed in the nozzle?

Density and pressure

A wooden cube of solid material is placed on a horizontal surface. What determines the pressure produced by the cube’s weight on the horizontal surface?

Density and pressure

Which formula could be used to calculate power?

Potential difference and power

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. In which stage of the jump are all three forms of energy greater than zero?

Energy conservation

An object is moved horizontally to the right in a uniform vertical gravitational field. Which statement describes how the gravitational potential energy of the object changes?

Gravitational potential energy and kinetic energy

A copper wire having a length of $3.6\,\text{m}$ and a diameter of $1.22\,\text{mm}$ is pulled by a force of $37\,\text{N}$. Hooke’s law applies to the wire. The Young modulus of copper is $1.17 \times 10^{11}\,\text{Pa}$. What extension is produced by this force?

Stress and strain

What are the SI base units for electromotive force (e.m.f.)?

Potential difference and power

For a spring with spring constant $k$, the spring follows Hooke’s law and stretches by $x$ when a force $F$ is applied to it. The elastic potential energy stored in the spring is $E_p$. The diagram depicts two such springs connected in parallel and suspended from a fixed beam. What are the extension and total elastic potential energy of this arrangement when the same force $F$ is applied?

Elastic and plastic behaviour

The diagram depicts a transverse wave on a rope. The wave is moving from left to right. At the moment shown, points P and Q on the rope have zero displacement and maximum displacement, respectively. Which row states the direction of motion, if any, of points P and Q at this instant?

Progressive waves

An electromagnetic wave in a vacuum has a period of $1.0\,\text{ns}$. Determine the wave’s frequency and wavelength.

Electromagnetic spectrum

An observer is standing on a railway platform. A train moves past the observer at a steady speed while its whistle emits sound with constant frequency $f$. What is heard by the observer?

Doppler effect for sound waves

Which microorganisms have a length equal to the free-space wavelength of an electromagnetic wave that can be seen by the human eye?

Electromagnetic spectrum

Two progressive waves are superposed. What essential condition must be met for the two waves to produce a stationary wave?

Stationary waves

In an experiment designed to create a stationary sound wave in air, a fine powder is first spread uniformly along the full length of a horizontal glass tube that is closed at one end. A loudspeaker at the open end of the tube sends in a sound wave with a fixed wavelength. A stationary wave then develops, and the powder gathers into evenly spaced heaps, as shown. Which statement explains where the powder heaps form inside the tube?

Stationary waves

A sound wave with wavelength $0.50\,\text{m}$ travels through a doorway that is $1.0\,\text{m}$ wide between two rooms. Which change would make the diffraction greater?

Diffraction

A light source is made up of a vertical slit that is lit by red light (R) and violet light (V). The wavelength of R is about twice the wavelength of V. A parallel vertical double slit is set up close by. A white screen is placed so that fringes are formed on it. Which graph most accurately shows the interference fringes formed on the screen?

Interference

Which characteristic of a light wave can be found using a diffraction grating?

The diffraction grating

A digital meter is being used to determine the current in an electric circuit. Its reading varies between $3.04\,\text{A}$ and $3.08\,\text{A}$. The meter readings are accurate to $\pm1\%$. What is the current’s true value, including its uncertainty?

Errors and uncertainties

An electric current flows through a copper wire. Which statement about the average drift speed of the charge carriers in the wire is correct?

Electric current

A battery having a fixed internal resistance is connected to a resistor with resistance $250\,\Omega$, as shown. For a period of $60\,\text{s}$, the current in the resistor is $40\,\text{mA}$. Over this interval, $6.0\,\text{J}$ of energy is dissipated by the internal resistance. How much energy is delivered to the external resistor during the $60\,\text{s}$, and what is the electromotive force (e.m.f.) of the battery?

Practical circuits

Which component is represented by the $I$-$V$ graph shown?

Resistance and resistivity

Two wires, P and Q, have equal resistance. Wire Q is made from a material whose resistivity is twice that of the material used for wire P. The diameter of wire Q is twice that of wire P. Find the ratio $\dfrac{\text{length of wire P}}{\text{length of wire Q}}$?

Resistance and resistivity

A voltmeter indicates $9.000\,\text{V}$ when it is placed across the battery terminals. If a resistor of resistance $11.0\,\Omega$ is then connected in parallel with the battery, the voltmeter reading becomes $8.800\,\text{V}$. What internal resistance does the battery have?

Potential difference and power

Each of Kirchhoff’s laws is associated with the conservation of a physical quantity. Which conserved physical quantities are applied when deriving Kirchhoff’s first law and Kirchhoff’s second law?

Kirchhoff's laws

In the circuit $PQR$ shown, three batteries and three identical resistors are connected together. The batteries have negligible internal resistance. What is the potential difference between points $P$ and $Q$?

Kirchhoff's laws

Cell $E$, with electromotive force (e.m.f.) $2\,\text{V}$ and negligible internal resistance, is joined to a uniform resistance wire with resistance $10\,\Omega$ and length $1.0\,\text{m}$. $Z$ is a connection that can be placed at any point along the resistance wire. A galvanometer is linked between $Z$ and point $Q$. A second source of e.m.f. of about $8\,\text{mV}$ is connected between points $P$ and $Q$. The e.m.f. of the second source is found by moving the position of $Z$ until the galvanometer shows zero. Which modification to the circuit would make it possible to obtain a much more accurate value for the e.m.f. of the second source?

Practical circuits

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

Atoms, nuclei and radiation

Nucleus $X$ undergoes $\beta^+$ decay. The resulting products are nucleus $Y$ with proton number $Z$, a $\beta^+$ particle, and a further particle $P$. $X \rightarrow Y + \beta^+ + P$. Which particle is $P$, and what is the proton number of nucleus $X$?

Atoms, nuclei and radiation

Which of the following quantities is a vector quantity?

Scalars and vectors

A particle is made up of two up quarks and one charm quark. What is its charge, written in units of the elementary charge $e$?

Fundamental particles

A stone is launched horizontally at time $t = 0$ and then drops. Air resistance can be ignored. The stone has a horizontal velocity component $v_H$ and a vertical velocity component $v_v$. Which graph shows how $v_H$ and $v_v$ change with time $t$?

Equations of motion

For an object falling from rest on the Earth, the time taken to travel a vertical distance $h$ is $T_E$. For the same object falling from rest on the Moon, the time taken to travel the same vertical distance $h$ is $T_M$. The ratio $\frac{\text{acceleration of free fall on the Earth}}{\text{acceleration of free fall on the Moon}}$ is equal to $6$. Air resistance is negligible for the object on the Earth and on the Moon. Determine the ratio $\frac{T_E}{T_M}$?

Equations of motion

A cyclist is riding in still air and pedals with maximum effort. She attains a top speed. Later, after some time, her top speed becomes higher. What could be one possible reason for this?

Equilibrium of forces

A ball with mass $0.5\,\text{kg}$ strikes a vertical wall at a speed of $12\,\text{m s}^{-1}$. It then rebounds along the same line at a speed of $8\,\text{m s}^{-1}$. The impact takes $0.10\,\text{s}$. What is the average force on the ball due to the collision?

Momentum and Newton's laws of motion

An air bubble is moving upward through a tank of water at terminal (constant) velocity. The forces acting on the bubble are $X$, $Y$ and $Z$, as shown. The upthrust on the bubble is $X$. Which statement about the forces is correct?

Equilibrium of forces