Oct/Nov 2021

What is necessary when noting down a measurement of a physical quantity?

SI units

A ball with mass $0.16\ \text{kg}$ is moving horizontally at a speed of $20\ \text{m s}^{-1}$. It strikes a wall and bounces back along the same line with a speed of $15\ \text{m s}^{-1}$. The ball remains in contact with the wall for $1.0\ \text{ms}$. What is the average force exerted by the wall on the ball?

Momentum and Newton's laws of motion

A uniform solid block is completely beneath the surface in a tank of water. The block has dimensions $x$ and $y$, as illustrated. It is kept vertical in the orientation shown. The density of the block is equal to the density of the water. If the block is maintained at the same depth $d$ below the water surface at all times, which single change would make the upthrust force on the block greater?

Density and pressure

Shelf XY is $0.40\,\text{m}$ in length and is fixed to a wall at end X. A wire, as shown, is attached to Y and to the wall to hold it horizontal. The wire carries a tension force of $15\,\text{N}$ at an angle of $30^{\circ}$ to the horizontal. What is the moment of this force about point X?

Turning effects of forces

A statement on the principle of moments has some words missing: ‘When an object is in rotational equilibrium, the total clockwise moments about any point are equal to the total anticlockwise moments about ................. .’ Which words complete the statement correctly?

Turning effects of forces

A bird plunges to a depth of $1.50\,\text{m}$ beneath the surface of a lake. Atmospheric pressure is $101\,\text{kPa}$. The density of water is $1000\,\text{kg m}^{-3}$. What is the pressure at this depth?

Density and pressure

Which statement about energy is incorrect?

Energy conservation

A pulley with a radius of $0.40\,\text{m}$ holds weights of $20\,\text{N}$ and $15\,\text{N}$ using a thin string, as illustrated. The weights are lifted by turning the pulley slowly clockwise through an angle of $60^{\circ}$. What is the rise in the total gravitational potential energy of the weights?

Gravitational potential energy and kinetic energy

A car with mass $1500\,\text{kg}$ speeds up from an initial velocity of $15\,\text{m s}^{-1}$. As a result of this acceleration, the car gains $3.0 \times 10^{5}\,\text{J}$ of kinetic energy. What is the increase in the car’s speed?

Gravitational potential energy and kinetic energy

A car with mass $1500\,\text{kg}$ moves downhill at a steady speed of $30\,\text{m s}^{-1}$. The slope makes an angle of $6.0^{\circ}$ with the horizontal, as illustrated. The size of the total resistive force on the car is $2000\,\text{N}$. Determine the power output of the car’s engine.

Equilibrium of forces

A metal wire with cross-sectional area $A$ and original length $l$ is subjected to stress $\sigma$. It consequently has strain $\epsilon$. Which expression gives the Young modulus of the metal?

Stress and strain

For electrons moving through a metal conductor, the mobility $\mu$ can be found from $\mu = \left(\frac{e}{m}\right) \tau$ where $e$ represents the charge of an electron and $m$ is the electron’s mass. The average interval between one electron colliding with the atoms in the metal and the next is $\tau$. What are the SI base units for $\mu$?

Electric current

Two identical springs are arranged in parallel. As shown, a weight of $8.0\,\text{N}$ is suspended from the pair. The graph gives the change in force with length for one of the springs. What is the strain energy stored in one of the springs?

Stress and strain

Two balls are floating at the sea surface. Their separation is $1.30\,\text{m}$. A wave propagates across the sea surface, making the balls oscillate vertically. The separation between a crest and the neighbouring trough of the wave is $0.90\,\text{m}$. What phase difference exists between the two balls?

Progressive waves

Which statement concerning transverse or longitudinal waves is incorrect?

Transverse and longitudinal waves

A glass tube is sealed at one end and fitted with a loudspeaker at the other, as shown. When the sound has frequency $f_0$, a stationary wave is produced with a node at the sealed end of the tube. No other nodes are present. The sound frequency is then gradually increased. What frequency of the sound gives the next stationary wave?

Stationary waves

For which waves can the Doppler effect be observed?

Doppler effect for sound waves

Which type of radiation could be made up of waves with wavelength $0.5\,\text{nm}$?

Electromagnetic spectrum

A string is stretched between point P and an oscillator M. A second string is stretched between M and point Q. M lies halfway between P and Q. The oscillator’s frequency is altered until stationary waves are produced on both strings. The wave speed on the section from P to M is twice the wave speed on the section from M to Q. Which diagram could show the stationary-wave arrangement?

Stationary waves

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

Diffraction

Light with wavelength $\lambda$ falls normally on two narrow slits $S_1$ and $S_2$, which are separated by a small distance. On a screen placed far from the slits, bright and dark fringes are seen. The $n$th dark fringe from the central bright fringe is found at point P on the screen. Which equation is valid for every positive value of $n$?

Interference

Green light falls normally on a diffraction grating and produces a diffraction pattern on a screen far away. Which change, on its own, would reduce the spacing between the diffraction maxima on the screen?

The diffraction grating

An aircraft is travelling at an angle $\theta$ east of north, with a horizontal velocity relative to the air of $800 \, \text{km h}^{-1}$. A wind is blowing horizontally from east to west at $200 \, \text{km h}^{-1}$, as illustrated. The aircraft's resultant velocity is directed due north. Find the value of angle $\theta$ and the size of the resultant velocity.

Scalars and vectors

What does the term electric field strength mean?

Potential difference and power

There are three parallel metal plates with identical area. The gap between the top plate and the middle plate is $2.0\,\text{cm}$, while the spacing between the middle plate and the bottom plate is $1.0\,\text{cm}$. The top plate is maintained at a potential of $+500\,\text{V}$, the middle plate at $+200\,\text{V}$ and the bottom plate is earthed, as shown. What is the value of the ratio $\frac{\text{magnitude of force on an electron at X}}{\text{magnitude of force on an electron at Y}}$?

Potential difference and power

The current $I$ in a wire is expressed by the equation $I = nAvq$ where $n$ is the number density of the free electrons, $A$ is the cross-sectional area of the wire, $v$ is the mean drift velocity of the free electrons and $q$ is the charge on an electron. Which relationship is not involved in deriving this equation?

Electric current

The diagram shows a circuit that includes two resistors, P and Q, together with a power supply whose internal resistance is negligible. The current through resistor P is $2.0\,\text{A}$, and resistor P dissipates $18\,\text{W}$ of power. Resistor Q loses $240\,\text{J}$ of energy when a charge of $40\,\text{C}$ flows through it. What is the electromotive force (e.m.f.) of the power supply?

Potential difference and power

The $I$-$V$ characteristics for two electrical components P and Q are displayed. Which statement is correct?

Resistance and resistivity

Wires S and T are two copper wires of the same length and are joined in parallel. The diameter of wire S is $3.0\,\text{mm}$. The diameter of wire T is $1.5\,\text{mm}$. A potential difference is applied across the two ends of this parallel combination. What is the value of the ratio $\frac{\text{current in S}}{\text{current in T}}$?

Resistance and resistivity

What circuit symbol represents an oscilloscope?

Practical circuits

The circuit shows three identical cells, each with electromotive force (e.m.f.) $E$ and internal resistance $r$. What potential difference exists between points X and Y?

Kirchhoff's laws

The potential differences in two resistors with resistances $R_1$ and $R_2$ are being compared by means of a potentiometer wire (a wire of uniform resistance) in the electrical circuit illustrated. One end of a galvanometer is attached to point X. The galvanometer shows zero when its other end is joined to a point located $60\,\text{cm}$ from one end of the potentiometer wire. One end of a second galvanometer is attached to point Y. This galvanometer shows zero when its other end is joined to a point located $80\,\text{cm}$ from the same end of the potentiometer wire. Determine the ratio $\frac{R_2}{R_1}$?

Practical circuits

A uranium-238 nucleus, $^{238}_{92}\text{U}$, passes through a sequence of nuclear decays to produce uranium-234, $^{234}_{92}\text{U}$. Which decay sequence could lead to this outcome?

Atoms, nuclei and radiation

A cathode-ray oscilloscope (CRO) is being used to show a sound wave with frequency $2000\ \text{Hz}$. The CRO trace is shown. What is the time-base setting of the CRO?

Progressive waves

What combination of up (u) and down (d) quarks makes a proton?

Fundamental particles

The following four possible sources of error are given for a set of measurements. 1 an analogue meter whose scale is viewed from different angles 2 a meter that always gives readings $5\%$ too high 3 a meter with a needle that is not frictionless, so the needle occasionally sticks slightly 4 a meter with a zero error Which errors are random and which are systematic?

Errors and uncertainties

An archer fires an arrow at a target. The diagram illustrates the path followed by the arrow. The effect of air resistance can be ignored. The graphs show the way in which three different quantities $p$, $q$ and $r$ change with time. Which quantity could represent the horizontal component of displacement, and which quantity could represent the vertical component of displacement of the arrow?

Equations of motion

At time $t = 0$, cars X and Y are placed as shown. Both cars move in the same direction. X is $50\ \text{m}$ behind Y and travels at a constant speed of $30\ \text{m s}^{-1}$. Y travels at a constant speed of $20\ \text{m s}^{-1}$. Find the value of $t$ when X is level with Y.

Equations of motion

A constant resultant force acts on an object in the same direction as the object’s velocity. Which graph might represent how the momentum $p$ of the object changes with time $t$?

Momentum and Newton's laws of motion

Which statement has to be correct for an object in a gravitational field?

Momentum and Newton's laws of motion

Which row indicates the requirement that every physical quantity must have?

Physical quantities

The table presents four separate collisions involving two blocks, each with mass $0.50\,\text{kg}$. Which one of the collisions is perfectly elastic?

Linear momentum and its conservation

A cylindrical piece of wood has cross-sectional area $A$ and weight $W$. It is fully submerged in water with its axis vertical. The block is acted on by pressures $p_t$ and $p_b$ at its upper and lower surfaces respectively. What is the upthrust on the block?

Density and pressure

As shown, two forces, each with magnitude $F$, act on a disc whose diameter is $s$. What torque is produced on the disc?

Turning effects of forces

A mass of $500\,\text{g}$ is fixed to one end of a rod with length $1.50\,\text{m}$. The rod is supported by a pivot that is $25\,\text{cm}$ from the opposite end. The rod is held horizontally. What is the moment about the pivot caused by the mass?

Turning effects of forces

Beam QR is supported in place by wire PQ. This arrangement is used to make a crane that carries a stationary load of $4.0\,\text{kN}$, as illustrated. What force does the beam QR exert on point Q?

Equilibrium of forces

A metal cylinder, fully submerged in water, is suspended from a newton meter. The cylinder has height $L$ and is lifted slowly upwards by raising the newton meter. As the cylinder’s base travels from line X in the water to line Y above the water surface, the reading $R$ on the newton meter is noted. The cylinder moves at constant speed. Which graph most accurately represents how $R$ changes with the distance $d$ of the cylinder’s base from line X?

Density and pressure

A ball is projected straight up into the air. It reaches the highest point of its motion before it starts to move straight down. Take the gravitational potential energy of the ball to be zero at the point where it is first released. Which statement about the ball is not correct?

Gravitational potential energy and kinetic energy

An object moves with constant velocity over a horizontal layer of ice. Friction is negligible. A constant horizontal force of $2.1\,\text{N}$ is then exerted on the object, as shown. After a short interval following the application of the force, the object arrives at point X, which is at a displacement of $4.0\,\text{m}$ from the position where the force was first applied. What is the work done by the force on the object as it moves to point X?

Energy conservation

The energy changes taking place in a power station that burns fossil fuel may be represented as shown. chemical energy $W \rightarrow$ thermal energy $X \rightarrow$ electrical energy $Y$ Which expression represents the efficiency of the power station?

Energy conservation

Car X is moving at half the speed of car Y. Car X has twice the mass of car Y. Which statement is correct?

Momentum and Newton's laws of motion

What is another way to express an energy of $43\,\text{dJ}$?

SI units

The combined weight of a motorbike and rider is $1800\,\text{N}$. The motorbike moves in a straight line at steady speed up a hill that is inclined at $30^\circ$ to the horizontal. The useful output power of the motorbike is $36\,000\,\text{W}$. The overall resistive force from air resistance and friction acting on the motorbike and rider is $2400\,\text{N}$. Calculate the speed of the motorbike.

Energy conservation

The three springs are positioned vertically, as illustrated. Springs P and Q are identical, and each has spring constant $k$. Spring R has spring constant $3k$. What is the rise in the total length of the arrangement when a force $W$ is applied as shown?

Elastic and plastic behaviour

A metal wire is fastened to a fixed support so that it hangs straight down. Masses are then added to the wire. Assume that the wire’s cross-sectional area stays constant. A stress-strain graph for the wire is drawn, as shown. What does the shaded area beneath the graph represent?

Stress and strain

The table shows descriptions and examples of waves. Which row is correct?

Transverse and longitudinal waves

A sound wave produced by a loudspeaker is sent back by a reflector along the same path. At first, the microphone is at point $X$, where the sound intensity is at a minimum, as shown. The microphone is then moved towards the reflector and goes through four further intensity minima before arriving at a fifth minimum at point $Y$. The distance $XY$ is $70.0\,\text{cm}$. Determine the wavelength of the sound.

Stationary waves

A train moves along a straight track with constant speed of $30\,\text{m s}^{-1}$. Its horn emits a continuous sound at frequency $2400\,\text{Hz}$. An observer is at rest beside the railway line. As the train comes towards the observer, passes him, and then recedes. The speed of sound is $340\,\text{m s}^{-1}$. What is the greatest difference between the frequencies of the sound heard by the observer?

Doppler effect for sound waves

A beam of electromagnetic waves has a frequency of $30\,\text{THz}$ and is travelling in a vacuum. To which region of the electromagnetic spectrum do these waves belong?

Electromagnetic spectrum

A stationary wave is formed on a string stretched between two fixed points separated by $1.35\,\text{m}$, as shown. The wave speed on the string is $450\,\text{m s}^{-1}$. Determine the frequency of oscillation of the stationary wave?

Stationary waves

A beam of laser light is aimed at a narrow slit. Once it passes out from the other side of the slit, the diffracted light then lands on a screen. What pattern of light is observed on the screen?

Diffraction

Two waves, each of fixed amplitude, meet and form an interference pattern. In that pattern, there are minima at particular points where the displacement remains zero at every moment. Which statement best describes the two waves?

Stationary waves

A tennis ball is struck so that it leaves the racket with velocity $v$ at an angle $\theta$ above the horizontal. Its vertical velocity component is $v_y$. What is the size of the horizontal component of $v$?

Equations of motion

A beam of light with wavelength $5.5 \times 10^{-7}\,\text{m}$ falls normally on a diffraction grating. The separation between the second-order diffraction maxima is $80^\circ$, as illustrated. Determine the number of lines per metre of the diffraction grating.

The diffraction grating

Four diagrams showing the electric field between two oppositely charged point charges are displayed. Which diagram shows the electric field lines correctly?

Electric current

A proton travels into the uniform electric field between two parallel vertical metal plates in a vacuum. One plate is held at $0\,\text{V}$ and the other at $+10\,\text{V}$, as shown. What immediate change does the electric field produce in the proton’s motion straight after it enters the field?

Potential difference and power

What is the definition of the coulomb?

Electric current

A battery with electromotive force (e.m.f.) $10\,\text{V}$ and internal resistance $5.0\,\Omega$ is attached to a $5.0\,\Omega$ load resistor. What change is observed when the $5.0\,\Omega$ load resistor is substituted by a $50\,\Omega$ load resistor?

Potential difference and power

The graphs illustrate how the current $I$ changes with potential difference $V$ for three circuit components: a metal wire kept at constant temperature, a semiconductor diode and a filament lamp. Which row gives the correct identification of these graphs?

Resistance and resistivity

A cell has an electromotive force (e.m.f.) of $6.0\,\text{V}$. Its internal resistance is negligible, and it is connected to a resistor. The potential difference (p.d.) across the resistor is also $6.0\,\text{V}$. Although the e.m.f. and the p.d. are equal in numerical value, they refer to different processes. Which statement about these different processes is correct?

Potential difference and power

A battery with negligible internal resistance is linked to three resistors, as illustrated. The potential difference across every resistor is $2\,\text{V}$. The current supplied by the battery is $0.4\,\text{A}$, and the current through one of the resistors in parallel is $0.3\,\text{A}$. What is the current through the other resistor in parallel, and what is the electromotive force (e.m.f.) of the battery?

Kirchhoff's laws

A battery with electromotive force (e.m.f.) $9.0\,\text{V}$ and internal resistance $1.0\,\Omega$ is joined to a fixed resistor of resistance $5.0\,\Omega$ and a potentiometer whose maximum resistance is $3.0\,\Omega$, as illustrated. The sliding contact on the potentiometer is then moved through its entire range of motion. What is the largest value of the potential difference measured by the voltmeter?

Potential dividers

An unstable nucleus undergoes decay by releasing a $\beta^{+}$ particle. Which statement is correct?

Atoms, nuclei and radiation

Each of four cathode-ray oscilloscope (CRO) screens shows a waveform. The screen and time-base setting for each CRO are given. Which screens display waveforms with the same frequency?

Progressive waves

Which statement is incorrect?

Physical quantities

A student records the time $T$ taken for a pendulum with length $l$ to make one full oscillation. The measurements are listed in the table. $l = 0.420 \pm 0.001\,\text{m}$ $T = 1.3 \pm 0.1\,\text{s}$ She applies the equation $T = 2\pi\sqrt{\frac{l}{g}}$ to find the acceleration of free fall $g$. What is the most suitable estimate of the percentage uncertainty in the value of $g$?

Errors and uncertainties

The graph illustrates how the velocity of a vehicle travelling in a straight line changes with time $t$. The vehicle is travelling at $4.0\,\text{m s}^{-1}$ and starts to accelerate at $t = 0$. What is the acceleration of the vehicle at $t = 3.0\,\text{s}$?

Equations of motion

A stone is thrown straight up from the ground with an initial speed of $15\,\text{m s}^{-1}$. Air resistance may be ignored. What maximum height does the stone reach?

Equations of motion

What does the term mass of an object mean?

Physical quantities

The diagram depicts two parachutists, X and Y, descending straight down. The combined mass of parachutist Y and his parachute is twice the combined mass of parachutist X and his parachute. At this instant, the air resistance acting on parachutist Y is twice the air resistance acting on parachutist X. Neither parachutist has yet attained his constant (terminal) velocity. Which statement compares the acceleration of Y with the acceleration of X?

Momentum and Newton's laws of motion

A paperback book has 210 sheets of paper (pages). The ruler reading for its thickness is shown. What is the average thickness of a single sheet of paper in the book?

Physical quantities

The diagram illustrates two spheres moving directly towards one another. Each sphere travels with speed $u$. One sphere has mass $2m$ and the other sphere has mass $m$. Which diagram shows the outcome of a perfectly elastic collision?

Linear momentum and its conservation

A spherical object is moving through water at a steady speed. Three forces act on the object. Which diagram, showing these three forces to scale, is correct?

Equilibrium of forces

A pair of forces forms a couple. Which statement about the two forces cannot be correct?

Turning effects of forces

A shop sign is attached at its upper edge to a rusty horizontal hinge. The sign remains in equilibrium, hanging at an angle of $25^\circ$ to the vertical, as shown. The sign is a square with side length $52\,\text{cm}$ and has uniform thickness. Its mass is $36\,\text{kg}$. What is the moment of the weight of the sign about the hinge?

Turning effects of forces

A uniform rod with length $200\text{ cm}$ is mounted so that it can pivot freely at point $P$. It is kept horizontal in equilibrium by a $60\text{ N}$ weight, which is attached to the rod by a string passing over a frictionless pulley. What is the weight of the rod?

Turning effects of forces

The diagram presents two blocks $X$ and $Y$. Block $X$ has edges each of length $a$. When block $X$ is put into a liquid of density $\rho$, with the shaded face level with the liquid surface, it experiences an upthrust $U$. Block $Y$ has horizontal sides measuring $a$ and $2a$ and a height of $\frac{1}{2}a$. Block $Y$ is placed in a liquid of density $2\rho$, again with the shaded face level with the liquid surface. What is the upthrust on block $Y$?

Density and pressure

A gas is trapped in a syringe, as illustrated. The gas starts with a volume of $2.00\text{ cm}^3$. The atmospheric pressure is $101\text{ kPa}$. When the gas is heated and expands to a volume of $6.00\text{ cm}^3$, what work does the gas do on the atmosphere?

Density and pressure

A mechanical device performs useful work at a rate of $X$ and loses energy at a rate of $Y$. Which expression represents the efficiency of this device?

Energy conservation

Car $P$ has kinetic energy $240\text{ kJ}$. Car $Q$ has half the mass and twice the speed of car $P$. What is the kinetic energy of car $Q$?

Gravitational potential energy and kinetic energy

An engine drives a water pump. In $1.0\text{ minute}$, the pump lifts $0.50\text{ m}^3$ of water from a depth of $30\text{ m}$. The pump operates with an efficiency of $70\%$. The density of water is $1000\text{ kg m}^{-3}$. What is the useful output power from the engine?

Gravitational potential energy and kinetic energy

Which SI base units are used to express the unit of resistance?

Resistance and resistivity

Which spring arrangement gives an overall spring constant of $8.0\text{ N m}^{-1}$?

Elastic and plastic behaviour

A metal wire is pulled until it breaks, and a force-extension graph is drawn. Which graph is labelled correctly with the elastic region, the plastic region and the area that represents the work done in stretching the wire to the point of breaking?

Elastic and plastic behaviour

A longitudinal wave moves along a long spring. The spring is shown at one moment. What is the wavelength of the wave?

Transverse and longitudinal waves

Which statement about waves is correct?

Progressive waves

A stationary sound wave is set up in a pipe with one end closed and the other end open. There are two antinodes on the wave, and one antinode lies at the open end of the pipe. The pipe has a length of $0.600\,\text{m}$. The speed of sound in the air column inside the pipe is $340\,\text{m s}^{-1}$. Determine the frequency of the sound wave.

Stationary waves

A train moves with a constant speed on a straight track. Its horn produces a sound with frequency $500\,\text{Hz}$. A person beside the track detects a sound with frequency $450\,\text{Hz}$. The speed of sound in air is $340\,\text{m s}^{-1}$. Determine the speed of the train and state whether it is moving towards or away from the person.

Doppler effect for sound waves

A surface that seems smooth has irregularities on it that are less than the wavelength of visible light. What is the approximate maximum size of the biggest irregularities on the surface?

Electromagnetic spectrum

Two progressive waves move in opposite directions and produce a stationary wave. The graph illustrates how displacement varies with distance $x$ for the stationary wave and for one of the two progressive waves at the same instant. What are the approximate displacements of the other progressive wave at positions J, K and L?

Stationary waves

Which diagram illustrates the diffraction of water waves in a ripple tank?

Diffraction

A screen shows interference fringes formed by double-slit interference with light of wavelength $600\,\text{nm}$. The fringe spacing is $4.0\,\text{mm}$ and the slit separation is $0.60\,\text{mm}$. How far is the double slit from the screen?

Interference

Which list is made up solely of scalar quantities?

Scalars and vectors

A beam of green light falls normally on a diffraction grating. A number of bright spots appear on a screen on the far side of the grating, as shown. Which pair of changes could produce bright spots at exactly the same angles as before?

The diffraction grating

Two metal plates positioned in parallel are held at electric potentials of $+800\,\text{V}$ and $+1300\,\text{V}$. Which diagram best shows the electric field in the region between the plates?

Potential difference and power

An electron is placed in a uniform electric field with field strength $1500\,\text{V m}^{-1}$. Calculate the acceleration of the electron caused by the electric field?

Potential difference and power

During a lightning strike, $1 \times 10^{20}$ electrons pass a point in a time interval of $30\,\mu\text{s}$. What is the average current in the lightning strike?

Electric current

A cell has an electromotive force (e.m.f.) of $6\,\text{V}$ and internal resistance $R$. An external resistor, also with resistance $R$, is connected across the cell, as illustrated. Power $P$ is dissipated in the external resistor. The cell is then swapped for another cell with an e.m.f. of $6\,\text{V}$ and negligible internal resistance. What is the new power dissipated in the external resistor?

Potential difference and power

A wire with a uniform cross-section has resistance $R$. A second wire is made from the same material. It is twice as long as the first wire and has a diameter that is twice as large. What is the resistance of the second wire?

Resistance and resistivity

The diagram illustrates two resistor networks. Find the ratio $\dfrac{\text{total resistance of network 1}}{\text{total resistance of network 2}}$?

Resistance and resistivity

The circuit diagram shows three cells with electromotive forces $3.0\,\text{V}$, $2.0\,\text{V}$ and $4.0\,\text{V}$ connected in series with a resistor of resistance $5.0\,\Omega$. The cells are assumed to have negligible internal resistance. What is the current $I$ in the circuit?

Practical circuits

When $\alpha$-particles are directed at a thin metal foil, most of the particles travel straight through, but a few are scattered through a large angle. Which alteration would increase the fraction of $\alpha$-particles scattered through a large angle?

Atoms, nuclei and radiation

A neptunium-236 nucleus contains $93$ protons and $143$ neutrons. It undergoes decay by releasing an $\alpha$-particle. The nucleus produced then emits a $\beta^{-}$ particle. Which diagram indicates the changes in the number $P$ of protons and the number $N$ of neutrons in these nuclei?

Atoms, nuclei and radiation

The output from a signal generator is linked to a cathode-ray oscilloscope (CRO). A trace appears on the screen. The CRO time-base is set to $2.00\,\text{ms cm}^{-1}$. What is the frequency of the signal?

Progressive waves

Which arrangement of quarks could not represent the quark makeup of the hadron illustrated? $p$ = proton $n$ = neutron $\Sigma^{-}$ = sigma particle of charge $-e$ $\Sigma^{+}$ = sigma particle of charge $+e$ $u$ = up quark $d$ = down quark $s$ = strange quark

Fundamental particles

A shelf is measured to have a width of $305\,\text{mm}$, but it is then discovered that the markings on the ruler used are $1.0\%$ farther apart than they should be. What type of measurement error is this, and what is the shelf’s actual width?

Errors and uncertainties

The graph illustrates how the acceleration of a car changes with time. What quantity is represented by the shaded area beneath the graph?

Equations of motion

A stone is launched horizontally from the edge of a cliff and then falls into the sea. Air resistance is negligible. Which statement about the motion of the stone is not correct?

Equations of motion

Water is sent through a hose-pipe at a rate of $90\,\text{kg per minute}$. The water leaves the hose-pipe horizontally at a speed of $20\,\text{m s}^{-1}$. What minimum force must a person holding the hose-pipe apply to stop it moving backwards?

Momentum and Newton's laws of motion

A skydiver exits a motionless balloon and descends straight down over a large distance. Which graph best shows how the skydiver’s acceleration $a$ changes with the distance $s$ she has travelled as she falls through the air?

Non-uniform motion