May/June 2018

What unit is used for stress?

Stress and strain

A horizontal metal bar PQ with a length of $50.0\,\text{cm}$ is hinged at P. The diagram shows the metal bar as seen from above. At end Q, two forces of $16.0\,\text{N}$ and $5.0\,\text{N}$ act in the horizontal plane, as shown in the diagram. What is the combined moment about P caused by the two forces?

Turning effects of forces

Blocks P, Q, R and S are made from materials with the same density. Block T is made from a material whose density is twice that of the material used for the other blocks. The cross-sectional area and the height of each block are shown. Which two blocks produce the same pressure on the ground?

Density and pressure

Two forces of equal magnitude $F$ act in parallel on a rod of length $5d$. Which diagram shows where the two forces should be applied to give the greatest torque on the rod?

Turning effects of forces

Liquid X and liquid Y are kept in large open tanks. Liquid X has a density of $800\ \text{kg m}^{-3}$ and liquid Y has a density of $1200\ \text{kg m}^{-3}$. At what depths will the pressures be the same?

Density and pressure

A train with a mass of $3.3 \times 10^{6}\ \text{kg}$ is travelling at constant speed up a slope that makes an angle of $0.64^{\circ}$ to the horizontal. The train’s engine has a useful output power of $14\ \text{MW}$. Assume that no frictional forces oppose the train’s motion. Calculate the speed of the train.

Gravitational potential energy and kinetic energy

A cannon-ball with mass $3.50\ \text{kg}$ is launched at a speed of $22.0\ \text{m s}^{-1}$ from a gun on a ship, positioned at a height of $6.00\ \text{m}$ above sea level. Its total energy is made up of the gravitational potential energy relative to the sea surface and the kinetic energy. Determine the total energy of the cannon-ball as it exits the gun?

Gravitational potential energy and kinetic energy

An aircraft is moving in horizontal flight with a constant velocity of $90\ \text{m s}^{-1}$. The diagram indicates some of the forces acting on it. The aircraft has a mass of $2000\ \text{kg}$. What is the power developed by the thrust force?

Equilibrium of forces

An electrical generator begins operating at time zero. The graph shows the total electrical energy produced in the first $5$ seconds. What is the greatest electrical power produced at any instant during these first $5$ seconds?

Potential difference and power

The diagram represents a wire with diameter $D$ and length $L$, fixed securely at one end between two blocks of wood. A load is then hung from the wire, causing it to increase in length by $x$. A second wire is made from the same material, but has diameter $2D$ and length $3L$. Both wires obey Hooke’s law. What is the extension of the second wire when the same load is applied?

Stress and strain

In an experiment, two wires are stretched, one brass and the other steel. During this experiment, both wires obey Hooke’s law. The Young modulus for brass is smaller than the Young modulus for steel. Which graph shows the way stress changes with strain for both wires in this experiment?

Stress and strain

Physical quantities may be grouped as vectors or scalars. Which pair of quantities contains two vectors?

Scalars and vectors

A transverse progressive wave is established on a string. The graph shows how the displacement of one point on this string varies with time. The distance $XY$ on the graph represents the …1… of the wave. $X$ and $Y$ have the same …2…. Which words correctly fill gaps 1 and 2?

Progressive waves

Which part of the electromagnetic spectrum contains waves with a frequency of $10^{7}\ \text{MHz}$?

Electromagnetic spectrum

In a longitudinal wave, the particles vibrate in a direction parallel to the direction in which the wave transfers energy. This wave may be shown on a graph of particle displacement against distance from the source. Which point on the graph marks the centre of a compression?

Transverse and longitudinal waves

What can be inferred from a table showing the wavelengths of waves in the electromagnetic spectrum?

Electromagnetic spectrum

A binary star is made up of two stars that orbit a shared centre. Light from one star is detected on the Earth. The measured frequency of the light changes from a minimum frequency $f_{\min}$ to a maximum frequency $f_{\max}$, as shown. The rotation rate of the binary star rises. How do $f_{\max}$ and $f_{\min}$ change?

Doppler effect for sound waves

A teacher arranges the apparatus shown to produce a double-slit interference pattern on the screen. Which modification to the apparatus will make the fringe spacing larger?

Interference

In the diagram, two wave sources, $S_1$ and $S_2$, are shown. Their oscillations have a phase difference of $180^{\circ}$. Each source produces a wave with wavelength $2.0\,\text{cm}$. By the time the wave from each source reaches point $P$, its amplitude is $x_0$. What is the amplitude of the oscillation at $P$?

Interference

A pipe that is sealed at one end has a loudspeaker at the open end. A stationary sound wave is set up in the air inside the pipe, and there is an antinode at the open end of the pipe. The pipe has a length of $0.85\,\text{m}$. The speed of sound in air is $340\,\text{m s}^{-1}$. Which frequency of sound from the loudspeaker would not set up a stationary wave?

Stationary waves

A particle carries a charge of $+2.0\,\text{mC}$ and is located in a vertical uniform electric field. The particle experiences an upward electric force of $1.0 \times 10^{-2}\,\text{N}$. What is the electric field strength?

Electric current

A charged particle is placed in the electric field between two horizontal metal plates that are connected to a battery, as illustrated. The electric field exerts a force $F$ on the particle. The gap between the plates is increased so that it is twice as large. What is the new force on the particle?

Potential difference and power

As illustrated, two dogs are dragging a sledge over an icy track. Dog X exerts a pull of $200\ \text{N}$ at an angle of $65^\circ$ to the front edge of the sledge. Dog Y exerts a pull of $120\ \text{N}$ at an angle of $45^\circ$ to the front edge of the sledge. What is the resultant forward force on the sledge exerted by the two dogs?

Scalars and vectors

The current $I$ in a metal wire is described by the expression below. $I = Anvq$ What is meant by the symbol $n$?

Electric current

The circuit diagrams each display two lamps $X$ and $Y$, and every lamp is connected to a cell. The current in lamp $X$ is $0.50\,\text{A}$ and its resistance is $9.6\,\Omega$. The current in lamp $Y$ is $3.0\,\text{A}$ and its resistance is $1.2\,\Omega$. Determine the ratio $\dfrac{\text{power in lamp }X}{\text{power in lamp }Y}$?

Potential difference and power

A cylindrical sample made of a soft material that conducts electricity has resistance $R$. It is rolled out so that its length becomes twice as large, while its volume remains unchanged. What will its new resistance be?

Resistance and resistivity

At a point in a circuit, the total current entering that point is equal to the total current leaving it. Which statement is correct?

Kirchhoff's laws

In the circuit diagram shown, the batteries are assumed to have negligible internal resistance. What are the values of the currents $I_1$, $I_2$ and $I_3$?

Kirchhoff's laws

A battery with an electromotive force (e.m.f.) of $6.0\,\text{V}$ and negligible internal resistance is linked to three resistors as illustrated. The resistance of each resistor is $4.0\,\text{k}\Omega$. What is the current in resistor $X$?

Practical circuits

A uniform resistance wire $XY$, with a length of $100\,\text{cm}$, is placed in series with a cell $L$. A further cell $M$ is put in series with resistors having resistances $5.00\,\Omega$, $10.0\,\Omega$ and $15.0\,\Omega$. The potential difference (p.d.) between $P$ and $Q$ is then balanced by $12.5\,\text{cm}$ of the resistance wire, causing the ammeter to show zero. After that, the p.d. across the remaining resistors is balanced using other lengths of the resistance wire. Which balanced lengths of resistance wire correspond to the connection points shown in the table?

Practical circuits

A motor has to be operated at a distance of $800\,\text{m}$ from its power supply. For it to work, the motor needs a potential difference (p.d.) of $16.0\,\text{V}$ and a current of $0.60\,\text{A}$. As shown, two wires are used to deliver power to the motor. Each wire has a resistance of $0.0050\,\Omega$ per metre. What minimum output p.d. must the power supply provide?

Potential difference and power

Which fundamental particle is a lepton?

Fundamental particles

How many down quarks are present in the nucleus of hydrogen-3, $^3_1\text{H}$?

Fundamental particles

For the circuit illustrated, an analogue ammeter is being recalibrated to act as a thermometer. The ammeter is linked in series with a thermistor. A thermistor is a component whose resistance changes with temperature. The graph indicates how the thermistor’s resistance $R$ varies as the temperature $T$ changes. Which diagram could show the temperature scale on the ammeter?

Practical circuits

Which equation is correct for $\beta^{-}$ decay?

Atoms, nuclei and radiation

A caliper is used to measure the edges of a cube. Each edge is found to have a length of $(30.0 \pm 0.1)\,\text{mm}$. These measurements are then applied to determine the volume of the cube. What is the percentage uncertainty in the calculated value of the volume?

Errors and uncertainties

A tennis ball is dropped and falls through the air from the top of a tall building. Which graph best shows how the distance $s$ fallen changes with time $t$?

Equations of motion

The graph illustrates how the weight of objects changes with mass on a certain planet. What is the value of the acceleration of free fall on the planet?

Momentum and Newton's laws of motion

The momentum of a car with mass $m$ rises from $p_1$ to $p_2$. What is the rise in the kinetic energy of the car?

Momentum and Newton's laws of motion

Two identical spheres, each with mass $m$ and moving at speed $v$, are travelling directly towards one another. They undergo a head-on elastic collision. Which statement is correct?

Linear momentum and its conservation

The thickness of a sheet of gold leaf is $0.125\,\mu\text{m}$. A gold atom has a radius of $174\,\text{pm}$. About how many atomic layers are present in the sheet?

Atoms, nuclei and radiation

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

Density and pressure

An astronaut launches a stone horizontally close to the Moon’s surface, where there is no atmosphere. Which row describes the horizontal and vertical forces acting on the stone after it has been released?

Momentum and Newton's laws of motion

A block of wood with a cylindrical shape has cross-sectional area $A$ and weight $W$. It is completely submerged in water, with its axis in a vertical position. The pressures acting on its top and bottom faces are $p_t$ and $p_b$ respectively. Which expression gives the upthrust acting on the block?

Density and pressure

A diving-board with uniform mass distribution is supported by two fixed rods at points P and Q. A person is standing at the end R of the diving-board, as illustrated. The forces produced by the rods on the board are vertical. The board stays in equilibrium while the person gradually moves from R towards point Q. Which row shows how the forces produced by the rods on the board change?

Turning effects of forces

Two forces, each with magnitude $F$, are applied to a rod in opposite directions. The point of application of each force is a distance $d$ from pivot $P$. What is the torque of this couple about $P$?

Turning effects of forces

The vector diagram illustrates three coplanar forces acting on an object at $P$. The magnitude of the resultant of these three forces is $1\,\text{N}$. What is the direction of this resultant force?

Equilibrium of forces

Under ‘normal driving conditions’, an electric car can cover $150\,\text{km}$ using the full $200\,\text{MJ}$ of energy held in its batteries. If the batteries begin fully charged, the car then travels $100\,\text{km}$ in ‘normal driving conditions’. The batteries are afterwards recharged from a household electrical supply that supplies a constant current of $13.0\,\text{A}$ at a potential difference of $230\,\text{V}$. Determine the minimum time needed to recharge the batteries?

Potential difference and power

The diagram depicts a ball of weight $W$ suspended in equilibrium by a string. The string makes an angle $\theta$ with the vertical. The tension in the string is $T$. A horizontal force $P$ from a metal rod keeps the ball away from the wall. What is the relationship between the magnitudes of $T$, $P$ and $W$?

Equilibrium of forces

A steel sphere is let go so that it falls straight down onto a level metal plate. It strikes the plate with speed $u$, rebounds from it with speed $v$, and rises vertically to half its initial height. Air resistance is to be ignored. Which expression gives the value of $\frac{v}{u}$?

Gravitational potential energy and kinetic energy

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

Gravitational potential energy and kinetic energy

The drag coefficient $C_d$ is a dimensionless quantity. It is used to compare the drag acting on different cars at different speeds. $C_d$ is defined by the equation $$C_d = \frac{2F}{v^n \rho A}$$ where $F$ represents the drag force on the car, $\rho$ is the density of the air, $A$ is the car’s cross-sectional area and $v$ is the speed of the car. What is the value of $n$?

Physical quantities

For an elastic material with Young modulus $E$, a tensile stress $S$ is applied. Hooke’s law is obeyed. What is the expression for the elastic energy stored per unit volume of the material?

Stress and strain

The graph plots how the length of a spring changes as the load applied to it increases. What is the spring constant of the spring?

Elastic and plastic behaviour

Two lasers produce light in a vacuum. One gives off red light and the other gives off green light. Which property of the two laser beams must be different?

Electromagnetic spectrum

The diagram illustrates the screen of a cathode-ray oscilloscope (c.r.o.) showing a wave. The time-base on the c.r.o. is adjusted to $10\ \text{ms\ per division}$. What is the frequency of the wave?

Progressive waves

One end of a string is clamped, while the opposite end is linked to a vibrator. The vibrator’s frequency is gradually raised from zero. This produces a sequence of stationary waves. Assume that point P is a node in a stationary wave. What are the first five wavelengths of the stationary waves that could be produced?

Stationary waves

Which region of the electromagnetic spectrum contains waves whose wavelength is $1000$ times shorter than that of visible light?

Electromagnetic spectrum

The diagram illustrates equipment used to determine the frequency of a sound wave. A sound wave with an unknown frequency is bounced back from a metal plate. A microphone positioned a distance $D$ from the metal plate measures the sound intensity. A minimum intensity is observed when $D = 12.0\ \text{cm}$. The plate is then shifted farther from the microphone until the next minimum is observed when $D = 15.0\ \text{cm}$. The speed of sound in air is $336\ \text{m s}^{-1}$. What is the frequency of the sound?

Stationary waves

An astronomer studies the light coming from a star that is receding from the Earth. For the light that is observed, which quantity has increased because of the star’s motion?

Doppler effect for sound waves

The diagram depicts a stationary wave, at time $t = 0$, that has been produced on a string held fixed between points P and S. The nodes of the stationary wave are located on the string at P, Q, R and S. At time $t = 0$, point X is moving downward. The points on the string oscillate with time period $T$ and a maximum amplitude of $2\ \text{cm}$. The displacement $s$ is taken to be positive upwards. Which graph most accurately shows how the displacement $s$ of point Y on the string changes with $t$?

Stationary waves

The apparatus illustrated is used in a two-source interference experiment. What is the principal function of the single slit?

Interference

A student records the current through a resistor and the potential difference (p.d.) across it. The current reading has an uncertainty of $4\%$ and the p.d. reading has an uncertainty of $1\%$. The student then determines the resistance of the resistor. What is the percentage uncertainty in the calculated resistance?

Errors and uncertainties

Two large metal plates X and Y are parallel to each other and are placed in a vacuum, as shown. Plates X and Y have charges that are equal in size and opposite in sign. What happens to the force on a positively charged particle as it moves from plate X to plate Y?

Potential difference and power

Four diagrams show the electric field between two point charges with opposite signs. Which diagram gives the correct arrangement of the electric field lines?

Scalars and vectors

An electrical supply has a power output of $2.4\,\text{kW}$ when the potential difference (p.d.) is $240\,\text{V}$. The two wires linking the supply to a kettle each have a resistance of $0.50\,\Omega$, as illustrated. Calculate the power delivered to the kettle and the p.d. across the kettle.

Practical circuits

Which graph illustrates how voltage $V$ varies with current $I$ for a semiconductor diode?

Resistance and resistivity

Four distinct resistors are connected in the arrangement shown. A current of $1.5\,\text{A}$ enters the network at junction X and exits at junction Y. What is the current in the resistor with resistance $30\,\Omega$?

Kirchhoff's laws

A cell with constant electromotive force sends a current $I$ through an external resistor of resistance $R$. The p.d. across the terminals of the cell is $V$. If the internal resistance $r$ of the cell becomes larger, what happens to $V$ and to $I$?

Practical circuits

For the circuits shown, the batteries are identical and each has negligible internal resistance. Every resistor has the same resistance. The diodes have zero resistance when they are conducting and infinite resistance when they are not conducting. In which circuit is the battery current largest?

Practical circuits

A thermistor is an electrical component whose resistance changes with temperature. Thermistor T is part of a fire alarm system. The alarm sounds when the potential difference between X and Y reaches $4.5\,\text{V}$. What is the resistance of T at the moment the alarm is triggered?

Potential dividers

During the $\alpha$-particle scattering experiment, a beam of $\alpha$-particles is directed at a thin sheet of gold foil. The majority of the $\alpha$-particles pass straight through, or are turned through only a small angle. A very small fraction are turned through more than $90^{\circ}$, so they appear to bounce back towards the source of the $\alpha$-particles. Which conclusion about the structure of atoms cannot be deduced from this experiment on its own?

Atoms, nuclei and radiation

Radon-211, $^{211}_{86}\text{Rn}$, francium-210, $^{210}_{87}\text{Fr}$, and radium-212, $^{212}_{88}\text{Ra}$, are three nuclides. For each nuclide, how many neutrons are present in its nucleus?

Atoms, nuclei and radiation

A student places a potential difference $V$ of $(4.0 \pm 0.1)\,\text{V}$ across a resistor with resistance $R$ of $(10.0 \pm 0.3)\,\Omega$ for a duration $t$ of $(50 \pm 1)\,\text{s}$. The student then finds the energy $E$ dissipated by using the equation shown below: $$E = \frac{V^2 t}{R} = \frac{4.0^2 \times 50}{10.0} = 80\,\text{J}.$$ What is the absolute uncertainty in the energy value calculated?

Errors and uncertainties

A neutron consists of one up (u) quark and two down (d) quarks. As the neutron decays into a proton, $\beta^-$-emission occurs. What change happens to the neutron’s quark arrangement because of the $\beta$-emission? (The symbol for a neutrino is $\nu_e$ and for an antineutrino is $\bar{\nu}_e$.)

Fundamental particles

The velocity of an object varies with time $t$ as illustrated. Which graph most accurately represents how the displacement $s$ of the object changes with time $t$?

Equations of motion

At time $t = 0$, a projectile is projected at an angle to the horizontal. It moves above horizontal ground, as illustrated. Take air resistance to be negligible. Which graph most accurately shows how the speed of the projectile changes with $t$ from launch until it reaches the ground?

Equations of motion

A sky-diver drops straight down from a helicopter and then reaches a constant (terminal) velocity. The graph indicates how the sky-diver’s speed $v$ changes with time $t$. Which graph shows how the distance $d$ fallen by the sky-diver varies with time $t$?

Non-uniform motion

A tennis ball with mass $55\,\text{g}$ moves horizontally at a speed of $30\,\text{m s}^{-1}$. It then strikes a wall and rebounds horizontally with a speed of $20\,\text{m s}^{-1}$. The ball remains in contact with the wall for $5.0 \times 10^{-3}\,\text{s}$. What is the average force exerted on the wall by the ball?

Momentum and Newton's laws of motion

An elastic collision takes place between two bodies $X$ and $Y$. The mass of body $X$ is $m$ and the mass of body $Y$ is $4m$. Before the collision, body $X$ moves with speed $v$, and after the collision it moves in the opposite direction with speed $\frac{3v}{5}$. Body $Y$ is at rest before the collision. What is the kinetic energy of body $Y$ after the collision?

Linear momentum and its conservation

Which is the most suitable description of a physical quantity?

Physical quantities

Four cuboids with the same lengths, breadths and heights are submerged in water. As shown, vertical rods keep the cuboids at the same depth and in matching orientations. Water has density $\rho$. Cuboid W is made from a material with density $4\rho$. Cuboid X is made from a material with density $2\rho$. Cuboid Y is made from a material with density $\rho$. Cuboid Z is made from a material with density $0.5\rho$. Which option is correct?

Density and pressure

A rectangular block of lead, with density $1.13 \times 10^{4}\,\text{kg m}^{-3}$, has edge lengths of $12.0\,\text{cm}$, $15.0\,\text{cm}$ and $10.0\,\text{cm}$. What is the greatest pressure the block can apply when it is placed on a table?

Density and pressure

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

Turning effects of forces

Full-fat milk is formed by combining fat-free milk with fat. A volume of $1.000 \times 10^{-3}\,\text{m}^3$ of full-fat milk has a mass of $1.035\,\text{kg}$. In this milk, $4.00\%$ of the volume is fat. The density of fat-free milk is $1.040 \times 10^{3}\,\text{kg m}^{-3}$. Calculate the density of the fat.

Density and pressure

A piston with cross-sectional area $A$ confines gas inside a cylinder. The piston is not frictionless. When the gas is heated, it expands and drives the piston back by distance $r$, moving it from position P to position Q. The gas column then has length $s$. Which expression gives the work done by the gas against the atmosphere during this expansion?

Density and pressure

Water from a reservoir is supplied to the turbine in a hydroelectric system at a rate of $510\,\text{kg s}^{-1}$. The reservoir lies $280\,\text{m}$ above the turbine level. The generator, which is driven by the turbine, produces an electrical output of current $205\,\text{A}$ at a potential difference of $5800\,\text{V}$. What is the efficiency of the system?

Gravitational potential energy and kinetic energy

A ball is projected straight up into the air. It reaches the highest point of its motion and then starts to move straight downwards. Assume that the ball’s gravitational potential energy is zero at the point where it starts. Which statement about the ball is not correct?

Gravitational potential energy and kinetic energy

An upward force of $1000\,\text{N}$ is required to raise the hook of a crane at constant velocity. The crane is then employed to lift a load with mass $1000\,\text{kg}$ at a constant velocity of $0.50\,\text{m s}^{-1}$. What power is required to lift the hook and the load?

Gravitational potential energy and kinetic energy

The following data relate to a steel wire on an electric guitar. Diameter $= 5.0 \times 10^{-4}\,\text{m}$ Young modulus $= 2.0 \times 10^{11}\,\text{Pa}$ Tension $= 20\,\text{N}$ The wire breaks and then contracts elastically. Assume that Hooke’s law applies to the wire. By what percentage does the length $l$ of a section of the wire shorten?

Stress and strain

The graph illustrates how a spring’s extension changes with the force applied to stretch it. What is the strain energy stored in the spring when the extension is $4.0\,\text{cm}$?

Elastic and plastic behaviour

Which pair contains a vector quantity and a scalar quantity?

Scalars and vectors

A displacement-distance graph for a transverse progressive wave is displayed. The phase difference between points $X$ and $Y$ may be written as $(180n)^{\circ}$. What is the value of $n$?

Progressive waves

The four graphs show a progressive wave travelling along a stretched string. Graphs A and B illustrate how displacement $d$ changes with distance $x$ along the string at a single instant. Graphs C and D illustrate how displacement $d$ changes with time $t$ at one fixed value of $x$. The markings on the graphs are meant to indicate the wavelength $\lambda$, the period $T$ and the amplitude $a$ of the wave, but just one graph has been labelled correctly. Which graph is correctly labelled?

Progressive waves

A cathode-ray oscilloscope (c.r.o.) is being used to find the frequency of a sound wave. The diagram displays the waveform on the screen. The time-base setting is $5.0\,\text{ms/div}$. Determine the frequency of the sound wave.

Progressive waves

A police car moves with a velocity of $30.0\,\text{m s}^{-1}$ directly towards an observer who is at rest. The car horn produces sound at a frequency of $2000\,\text{Hz}$. The speed of sound is $340\,\text{m s}^{-1}$. What is the frequency of the sound received by the observer?

Doppler effect for sound waves

A vibrating tuning fork is placed above a measuring cylinder, as illustrated. Water is then added slowly into the measuring cylinder. The first much louder sound is heard when the water surface is $2.9\,\text{cm}$ above the base of the measuring cylinder. A second much louder sound is heard when the water surface reaches $67.3\,\text{cm}$ above the base. The speed of sound in air is $330\,\text{m s}^{-1}$. What is the frequency of the tuning fork?

Stationary waves

A water wave in a ripple tank undergoes diffraction when it travels through a gap in a barrier. Which two factors determine the angle of diffraction of the wave?

Diffraction

A double-slit interference pattern produced with red light of wavelength $7.0 \times 10^{-7}\,\text{m}$ gives a fringe spacing of $3.5\,\text{mm}$. For the same arrangement of apparatus, what fringe spacing would be seen if blue light with wavelength $4.5 \times 10^{-7}\,\text{m}$ is used instead?

Interference

Two parallel metal plates are placed $20\,\text{cm}$ apart in a vacuum. They are linked to two sources of potential difference, as illustrated. A proton is released in the region between the plates. What are the magnitude and direction of the proton's acceleration?

Potential difference and power

A particle of mass $m$ and charge $+q$ is projected into a uniform electric field with speed $v$. At the start, its velocity is at right angles to the electric field. As it passes through the field, it is displaced by distance $d$, as shown. A second particle with mass $2m$, charge $+q$ and speed $v$ enters the electric field along the same route. What distance is this particle deflected by in the electric field?

Equations of motion

What is one possible charge that a particle can have?

Atoms, nuclei and radiation

A force $F$ is acting at an angle $\theta$ above the horizontal. What are its horizontal component and its vertical component?

Scalars and vectors

A germanium slice with cross-sectional area $1.0\,\text{cm}^2$ carries a current of $56\,\mu\text{A}$. The charge-carrier number density in the germanium is $2.0 \times 10^{13}\,\text{cm}^{-3}$. Each charge carrier has a charge equal to that of an electron. What is the mean drift velocity of the charge carriers in the germanium?

Electric current

A cell with electromotive force (e.m.f.) $E$ and internal resistance $r$ is linked to an external resistor of resistance $R$, as illustrated. What is the power dissipated in the external resistor?

Potential difference and power

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

Resistance and resistivity

A metal wire with a length of $1.4\,\text{m}$ has a constant cross-sectional area of $7.8 \times 10^{-7}\,\text{m}^2$. The metal’s resistivity is $1.7 \times 10^{-8}\,\Omega\,\text{m}$. What is the wire’s resistance?

Resistance and resistivity

A battery with an electromotive force (e.m.f.) of $6.0\,\text{V}$ and negligible internal resistance is linked to three resistors, each having resistance $6.0\,\Omega$. Which circuit would give a current of $0.67\,\text{A}$ through the battery?

Practical circuits

The diagram illustrates a circuit arrangement containing three resistors. Two of them, labelled $R$, are the same. The remaining resistor has a resistance of $5.0\,\Omega$. The resistance between Y and Z is determined to be $2.5\,\Omega$. What is the resistance between X and Y?

Kirchhoff's laws

The diagram displays a battery, a fixed resistor, an ammeter and a variable resistor joined in series. A voltmeter is connected across the fixed resistor. The resistance of the variable resistor is decreased. Which row shows how the readings on the ammeter and the voltmeter change?

Potential dividers

The circuit diagram depicts a battery with electromotive force (e.m.f.) $9.0\,\text{V}$ and negligible internal resistance. It is linked to two resistors with resistances $160\,\Omega$ and $R$. The output potential difference $V_{\text{out}}$ is $4.0\,\text{V}$. Determine the resistance $R$.

Potential dividers

For the circuit diagram shown, XY is a length $L$ of uniform resistance wire. A potential difference is applied across XY. $R_1$ and $R_2$ are unknown resistors. J is a sliding contact that connects the junction of $R_1$ and $R_2$ to positions on XY through a lamp S. J is shifted along XY until the lamp is not lit. This position is a distance $x$ from X. The potential difference across $R_1$ is $V_1$ and the potential difference across $R_2$ is $V_2$. What is the value of the ratio $\dfrac{V_1}{V_2}$?

Potential dividers

The nuclear equation below shows a magnesium-23 nucleus undergoing $\beta^+$ decay: $^{23}_{12}\text{Mg} \rightarrow X + \beta^+ + \nu_e$. What is the identity of nucleus X?

Atoms, nuclei and radiation

What can be done to reduce systematic errors during a measurement?

Errors and uncertainties

Which list is made up entirely of leptons?

Fundamental particles

In an investigation to find the Young modulus $E$ of the material in a wire, the measurements recorded are shown below. Mass suspended from the wire end: $m = 2.300 \pm 0.002\,\text{kg}$ Initial length of wire: $l = 2.864 \pm 0.005\,\text{m}$ Wire diameter: $d = 0.82 \pm 0.01\,\text{mm}$ Wire extension: $e = 7.6 \pm 0.2\,\text{mm}$ The Young modulus is found from $E = \dfrac{4mgl}{\pi d^2 e}$ where $g$ represents the acceleration of free fall. The obtained value of $E$ is $1.61 \times 10^{10}\,\text{N m}^{-2}$. In what form should the value of $E$ and its uncertainty be written?

Stress and strain

A rock on the surface of Mars is thrown straight upwards with an initial speed of $9.4\,\text{m s}^{-1}$. It reaches a maximum height of $12\,\text{m}$ above the surface. Assume that Mars has no atmosphere. What is the acceleration of free fall near the surface of Mars?

Equations of motion

Two masses, $M$ and $m$, are joined by an inextensible string that runs over a frictionless pulley. Mass $M$ is placed on a frictionless slope, as illustrated. The slope makes an angle $\theta$ with the horizontal. At first, the two masses are held at rest, and they are then released. Mass $M$ travels down the slope. Which expression is necessarily true?

Momentum and Newton's laws of motion

At time $t = 0$, a sky-diver leaves a balloon that is stationary. During the descent, her speed and the air resistance both increase until the air resistance force is equal to her weight. Which graph best indicates how displacement $s$ changes with time $t$ for the sky-diver’s motion?

Non-uniform motion

A ball with mass $0.20\,\text{kg}$, moving in the $x$-direction at speed $0.50\,\text{m s}^{-1}$, strikes a ball of mass $0.30\,\text{kg}$ that is moving in the $y$-direction at speed $0.40\,\text{m s}^{-1}$. After the collision, the two balls remain stuck together and move at an angle $\theta$ to the $x$-direction. What is the value of $\theta$?

Linear momentum and its conservation