Oct/Nov 2013

Which row gives an SI base quantity together with the correct unit?

SI units

An astronaut with mass $m$ is inside a spacecraft and, while it is at rest on the launchpad, experiences a gravitational force of $F = mg$. What is the gravitational force acting on the astronaut when the spacecraft is launched vertically upwards with an acceleration of $0.2g$?

Momentum and Newton's laws of motion

A stream of $\alpha$-particles strikes a lead sheet. Every $\alpha$-particle in the stream has a mass of $6.6 \times 10^{-27}\ \text{kg}$ and a speed of $1.5 \times 10^{7}\ \text{m s}^{-1}$. $5.0 \times 10^{4}$ $\alpha$-particles per second strike an area of $1.0\ \text{cm}^{2}$ of lead. Nearly all of the $\alpha$-particles are absorbed by the lead, so their speed after collision is zero. What is an estimate of the average pressure exerted on the lead by the $\alpha$-particles?

Momentum and Newton's laws of motion

An object in air is launched upwards and to the left. Which diagram shows the force(s) acting on the body when it is at its highest point?

Momentum and Newton's laws of motion

A particle is placed in a uniform field. The force on the particle acts in the direction opposite to the field. What field is the particle in, and which property of the particle does the field act on?

Electric current

An archer draws the bowstring back to position X. The bowstring and arrow are shown, together with the tension $T$ in the string. He then pulls the bowstring back further to position Y. When the arrow is released from position Y, the resultant force on it is greater. What is the increase in force?

Momentum and Newton's laws of motion

A metre rule of uniform construction, with a weight of $2.0\,\text{N}$, is balanced on a pivot at the $60\,\text{cm}$ mark. A $4.0\,\text{N}$ load is hung from one end, so that the rule turns around the pivot. When the rule is in the horizontal position, what is the total turning moment about the pivot?

Turning effects of forces

What does the term internal energy of a system mean?

Energy conservation

A barrel with weight $1.0 \times 10^3\,\text{N}$ is shown on a frictionless slope that is inclined at $30^\circ$ to the horizontal. A force is used to push the barrel so that it moves up the slope at constant speed. This force acts parallel to the slope. What is the work done in moving the barrel a distance of $5.0\,\text{m}$ up the slope?

Gravitational potential energy and kinetic energy

A car moving along a level road at a constant $20\,\text{m s}^{-1}$ while acting against a constant resistive force produces a power output of $40\,\text{kW}$. What is the magnitude of the resistive force?

Equilibrium of forces

A turbine in a hydroelectric power station is located $30\,\text{m}$ beneath the surface level of a large lake. Water flows through the turbine at a rate of $340\,\text{m}^3$ per minute. The turbine and generator system has an overall efficiency of $90\%$. What is the power output of the power station? (The density of water is $1000\,\text{kg m}^{-3}$.)

Gravitational potential energy and kinetic energy

A pendulum bob is kept at rest by a horizontal force $H$. The three forces acting on the bob are illustrated in the diagram. The tension in the pendulum string is $T$. The weight of the pendulum bob is $W$. Which of the following statements is correct?

Equilibrium of forces

The four brief paragraphs below describe the molecules in a beaker of water at $50^\circ\text{C}$. Which paragraph gives the correct description of the molecules?

Atoms, nuclei and radiation

Which two substances are usually both crystalline?

Elastic and plastic behaviour

The water in a bath has a depth that changes from $20.0\,\text{cm}$ at the shallow end to $30.0\,\text{cm}$ at the end where the plug is fitted. The density of the water is $1000\,\text{kg m}^{-3}$. What is the pressure exerted by the water on the plug?

Density and pressure

What properties most accurately describe modelling clay?

Elastic and plastic behaviour

A steel spring has a spring constant of $150\,\text{N m}^{-1}$. If a $25\,\text{N}$ weight is suspended from the spring, its stretched length becomes $55\,\text{cm}$. What was the spring’s original length?

Elastic and plastic behaviour

The diagram gives a sketch of a wave pattern over a short time interval. Which statement correctly describes this wave?

Progressive waves

Which statement correctly describes a light wave and a sound wave?

Transverse and longitudinal waves

A loudspeaker positioned above a tube makes the air in the tube resonate. A stationary wave is produced with two nodes and two antinodes, as shown. The speed of sound in air is $330\,\text{m s}^{-1}$. What is the frequency of the sound?

Stationary waves

A beam of light with wavelength $\lambda$ is incident on a diffraction grating whose slit spacing is $d$. A sequence of lines appears on a screen. What is the angle $\alpha$ between the two first order lines?

The diffraction grating

A student links two loudspeakers to a signal generator. As the student moves from P to Q, the loudness of the sound is seen to increase and decrease again and again. What causes the loudness of the sound to change?

Interference

The drag coefficient $C_d$ is a quantity with no units. It is used to compare the drag on different cars at different speeds. It is defined by the equation $C_d = \frac{2F}{\rho v^{n} A}$ where $F$ denotes the drag force on the car, $\rho$ represents the density of the air, $A$ is the cross-sectional area of the car and $v$ is the speed of the car. Determine the value of $n$.

Physical quantities

If plane-polarised light with amplitude $A$ is incident on a polarising filter, as illustrated, the amplitude of the transmitted light is $A \cos \theta$. The intensity of the original beam is $I$. Determine the intensity of the transmitted light when $\theta$ is $60.0^\circ$?

Polarisation

A pair of vertical conducting plates $X$ and $Y$ are arranged with a separation of $6.0\,\text{mm}$ in air. The $60\,\text{V}$ d.c. supply is connected as shown. What is the electric field strength at $E$, the point halfway between the plates?

Potential difference and power

A pair of parallel metal plates is maintained at a potential difference of $12\,\text{V}$. The separation between the plates is $1.0\,\text{mm}$. What is the electric field strength between the plates, and how much work is done on a charge of $+3.9\,\mu\text{C}$ when the charge is moved from the negative plate to the positive plate?

Potential difference and power

The diagram represents an electric circuit where the external resistor has resistance $2R$ and the source has internal resistance $R$. What is the ratio $\dfrac{\text{power in external resistor}}{\text{power in internal resistance}}$?

Potential difference and power

Two lamps are linked in series to a $250\,\text{V}$ power supply. One lamp has a rating of $240\,\text{V},\,60\,\text{W}$ and the other has a rating of $10\,\text{V},\,2.5\,\text{W}$. Which statement best describes the outcome?

Potential difference and power

A wire used in a heating element has resistance $R$. It snaps and is then swapped for another wire. The table lists the data for the original wire and the new wire. For the original wire, the length is $l$, the diameter is $d$ and the resistivity is $\rho$. For the new wire, the length is $l$, the diameter is $2d$ and the resistivity is $2\rho$. What is the resistance of the new wire?

Resistance and resistivity

In the circuit shown below, $P$ is a potentiometer with a total resistance of $10\,\Omega$ and $Q$ is a fixed resistor with a resistance of $10\,\Omega$. The battery has an electromotive force (e.m.f.) of $4.0\,\text{V}$ and negligible internal resistance. The voltmeter has a very high resistance. The slider on the potentiometer is then shifted from $X$ to $Y$, and a graph of voltmeter reading $V$ is drawn against slider position. Which graph would be obtained?

Potential dividers

A $2\,\Omega$ resistor and a $4\,\Omega$ resistor are joined to a cell. Which graph illustrates how the potential $V$ changes with distance between $X$ and $Y$?

Potential dividers

A network is made by connecting four resistors with resistances $R$, $2R$, $3R$ and $4R$. As illustrated, a battery with negligible internal resistance and a voltmeter are attached to the resistor network. The voltmeter shows $2\,\text{V}$. What is the electromotive force (e.m.f.) of the battery?

Potential dividers

When $\alpha$-particles are directed at a thin metal foil, most of the particles travel straight through, although a small number are scattered through a large angle. Which change would raise the proportion of $\alpha$-particles scattered through a large angle?

Atoms, nuclei and radiation

A periodic signal is shown on the screen of a cathode-ray oscilloscope. The screen is marked in $1\ \text{cm}$ squares, and the time base is adjusted to $2.00\ \text{ms cm}^{-1}$. What is the frequency of this periodic signal?

Practical circuits

Plutonium-239 ($^{{239}}_{{94}}\text{Pu}$) undergoes decay by emitting $\alpha$-radiation. Which nuclide is produced in one of these decay processes? (The product nuclides are denoted by $X$.)

Atoms, nuclei and radiation

A micrometer screw gauge is used to determine the diameter of a small steel sphere of uniform composition. The micrometer reading is $5.00\ \text{mm} \pm 0.01\ \text{mm}$. What is the percentage uncertainty in a calculation of the sphere’s volume, using these values?

Errors and uncertainties

One object travels straight from $P$ to $R$. Another object takes a shorter time but goes from $P$ to $Q$ and then on to $R$. Which statement is correct for the two objects during the trip from $P$ to $R$?

Scalars and vectors

The graph illustrates the way velocity $v$ changes with time $t$ for a bungee jumper. At which point is the bungee jumper briefly at rest, and at which point is her acceleration zero?

Equations of motion

An aircraft has an average speed of $600\ \text{km h}^{-1}$ on the outward journey and $400\ \text{km h}^{-1}$ on the return journey for the same distance. What is the average speed for the whole journey?

Non-uniform motion

What is meant by the mass of an object and by its weight on the Earth?

Physical quantities

Which row gives an SI base quantity together with its correct unit?

SI units

For an astronaut of mass $m$ inside a spacecraft, the gravitational force is $F = mg$ when the spacecraft is at rest on the launchpad. What is the gravitational force on the astronaut if the spacecraft is launched vertically upwards with an acceleration of $0.2g$?

Momentum and Newton's laws of motion

A stream of $\\alpha$-particles hits a lead sheet. The mass of each $\\alpha$-particle in the beam is $6.6 \\times 10^{-27}\,\\text{kg}$, and its speed is $1.5 \\times 10^{7}\,\\text{m s}^{-1}$. Every second, $5.0 \\times 10^{4}$ $\\alpha$-particles strike an area of $1.0\,\\text{cm}^2$ of lead. Nearly all of the $\\alpha$-particles are absorbed by the lead, so their speed after the collision is zero. What estimate can be made of the average pressure exerted on the lead by the $\\alpha$-particles?

Momentum and Newton's laws of motion

An object in air is projected upwards and to the left. Which diagram shows the force(s) acting on the body when it reaches its highest point?

Momentum and Newton's laws of motion

A particle is located in a uniform field. It experiences a force in the direction opposite to the field. Which field is the particle in, and which property of the particle is being acted on by the field?

Electric current

An archer pulls the bowstring back to position X. A diagram shows the bowstring and arrow, together with the tension $T$ in the string. He then pulls the bowstring back even further to position Y. The resultant force acting on the arrow is larger when the arrow is released from position Y. By how much does the force increase?

Equilibrium of forces

A uniform metre rule weighing $2.0\,\text{N}$ is supported on a pivot at the $60\,\text{cm}$ mark. A weight of $4.0\,\text{N}$ is hung from one end, so the rule turns about the pivot. When the rule is level, what is the resultant turning moment about the pivot?

Turning effects of forces

How is the internal energy of a system defined?

Energy conservation

The diagram represents a barrel with weight $1.0 \times 10^3\,\text{N}$ on a frictionless slope that is inclined at $30^\circ$ to the horizontal. A force is used to move the barrel up the slope at constant speed. This force acts parallel to the slope. What is the work done in moving the barrel through a distance of $5.0\,\text{m}$ up the slope?

Gravitational potential energy and kinetic energy

A car moving along a level road at a constant $20\,\text{m s}^{-1}$ while opposing a constant resistive force produces a power of $40\,\text{kW}$. What is the size of the resistive force?

Energy conservation

At a hydroelectric power station, a turbine is located $30\,\text{m}$ beneath the surface of a large lake. Water flows through the turbine at a rate of $340\,\text{m}^3$ per minute. The turbine and generator system has an overall efficiency of $90\%$. Determine the output power of the power station. (The density of water is $1000\,\text{kg m}^{-3}$.)

Gravitational potential energy and kinetic energy

A horizontal force $H$ keeps a pendulum bob at rest. The diagram shows the three forces acting on the bob. The tension in the pendulum string is $T$. The weight of the pendulum bob is $W$. Which statement is correct?

Equilibrium of forces

Presented here are four brief paragraphs about the molecules in a beaker of water at $50^\circ\text{C}$. Which paragraph gives the correct description of the molecules?

Atoms, nuclei and radiation

Which two substances are typically crystalline?

Elastic and plastic behaviour

The water in a bath has a depth that changes from $20.0\,\text{cm}$ at the shallow end to $30.0\,\text{cm}$ at the end with the plug. The density of the water is $1000\,\text{kg m}^{-3}$. Determine the pressure exerted by the water on the plug.

Density and pressure

Which characteristics best describe modelling clay?

Elastic and plastic behaviour

A steel spring has a spring constant of $150\,\text{N m}^{-1}$. If a $25\,\text{N}$ weight is attached to the spring, its length becomes $55\,\text{cm}$. What was the spring’s original length?

Elastic and plastic behaviour

The diagram depicts a sketch of a wave pattern over a brief time interval. Which statement correctly describes this wave?

Progressive waves

Which statement about a light wave and a sound wave is correct?

Transverse and longitudinal waves

A loudspeaker positioned above a tube makes the air in the tube resonate. A stationary wave is produced with two nodes and two antinodes, as shown. The speed of sound in air is $330\,\text{m s}^{-1}$. What frequency does the sound have?

Stationary waves

Light of wavelength $\lambda$ is incident on a diffraction grating with slit spacing $d$. A set of lines is seen on a screen. What angle $\alpha$ is formed between the two first order lines?

The diffraction grating

A student links two loudspeakers to a signal generator. While the student moves from P to Q, he observes that the loudness of the sound increases and decreases again and again. What makes the loudness of the sound change?

Interference

The drag coefficient $C_d$ is a quantity with no units. It is used to compare the drag on different cars at different speeds. It is defined by the equation $C_d = \\frac{2F}{\\rho v^n A}$, where $F$ is the drag force on the car, $\\rho$ is the density of the air, $A$ is the cross-sectional area of the car and $v$ is the speed of the car. Determine the value of $n$?

Physical quantities

When plane-polarised light with amplitude $A$ is sent through a polarising filter as illustrated, the emerging light has amplitude $A \cos \theta$. The intensity of the incident beam is $I$. What is the intensity of the light emerging when $\theta$ is $60.0^\circ$?

Polarisation

Two vertical conducting plates X and Y are arranged with a separation of $6.0\,\text{mm}$ in air. A $60\,\text{V}$ d.c. supply is connected as shown. What is the electric field strength at E, which is halfway between the plates?

Potential difference and power

A potential difference of $12\,\text{V}$ is applied across two parallel metal plates. The separation of the plates is $1.0\,\text{mm}$. Find the electric field strength between the plates and the work done on a charge of $+3.9\,\mu\text{C}$ when it is moved from the negative plate to the positive plate.

Potential difference and power

An electric circuit is illustrated in the diagram. The external resistor has resistance $2R$, and the source has internal resistance $R$. What is the ratio $\dfrac{\text{power in external resistor}}{\text{power in internal resistance}}$?

Potential difference and power

Two lamps are connected in series to a $250\,\text{V}$ power supply. One lamp has a rating of $240\,\text{V},\,60\,\text{W}$ and the other has a rating of $10\,\text{V},\,2.5\,\text{W}$. Which statement best describes the outcome?

Potential difference and power

The wire in a heating element has resistance $R$. It breaks and is swapped for another wire. The data for the original wire and the replacement wire are shown: the original wire has length $l$, diameter $d$, resistivity $\rho$; the replacement wire has length $l$, diameter $2d$, resistivity $2\rho$. What is the resistance of the replacement wire?

Resistance and resistivity

For the circuit shown, P is a potentiometer with total resistance $10\,\Omega$ and Q is a fixed resistor with resistance $10\,\Omega$. The battery has an electromotive force (e.m.f.) of $4.0\,\text{V}$ and negligible internal resistance. The voltmeter has a very high resistance. The slider on the potentiometer is shifted from X to Y, and a graph of voltmeter reading $V$ is drawn against slider position. Which graph would be obtained?

Potential dividers

A $2\,\Omega$ resistor and a $4\,\Omega$ resistor are linked to a cell. Which graph shows the way the potential $V$ changes with distance between X and Y?

Potential dividers

Four resistors with resistances $R$, $2R$, $3R$ and $4R$ are arranged to make a network. As shown, a battery with negligible internal resistance and a voltmeter are connected to the resistor network. The voltmeter shows a reading of $2\,\text{V}$. Find the electromotive force (e.m.f.) of the battery.

Kirchhoff's laws

When $\alpha$-particles are directed at a thin sheet of metal foil, the majority travel straight through, although a small number are scattered through a large angle. Which alteration would raise the proportion of $\alpha$-particles scattered through a large angle?

Atoms, nuclei and radiation

A periodically repeating signal is shown on the screen of a cathode-ray oscilloscope. The screen is divided into $1\,\\text{cm}$ squares, and the time base is adjusted to $2.00\,\\text{ms cm}^{-1}$. What is the frequency of this periodic signal?

Practical circuits

Plutonium-239 ($^{239}_{94}\text{Pu}$) undergoes decay by releasing $\alpha$-radiation. Which nuclide is produced in one of these decay equations? (The product nuclides are shown as X.)

Atoms, nuclei and radiation

A micrometer screw gauge is employed to determine the diameter of a small uniform steel sphere. The micrometer reading is $5.00\,\\text{mm} \\pm 0.01\,\\text{mm}$. What is the percentage uncertainty in a calculation of the sphere’s volume, using these values?

Errors and uncertainties

One object travels straight from P to R. A second object goes from P to Q to R in less time. Which statement is correct for the two objects on the trip from P to R?

Scalars and vectors

The graph illustrates how velocity $v$ changes with time $t$ for a bungee jumper. At which point is the bungee jumper momentarily at rest, and at which point is her acceleration zero?

Equations of motion

An aeroplane flies outward at an average speed of $600\,\\text{km h}^{-1}$ and then comes back at $400\,\\text{km h}^{-1}$ along the same distance. What is the average speed for the complete journey?

Equations of motion

What do the terms mass and weight of an object on the Earth mean?

Physical quantities

Which estimate seems realistic?

Physical quantities

A thorium nucleus $^{230}_{90}\text{Th}$, while moving, emits an $\alpha$-particle without any external cause. The product is a radium nucleus $^{226}_{88}\text{Ra}$, as illustrated. Which statement is correct?

Atoms, nuclei and radiation

An isolated system contains two bodies on which no external forces are acting. The two bodies collide with each other and remain joined after the impact. Which row gives the correct comparison of the total kinetic energy and the total momentum of the bodies before and after the collision?

Linear momentum and its conservation

A mass accelerates uniformly when the resultant force acting on it stays constant

Momentum and Newton's laws of motion

A lead pellet with mass $10.0\,\text{g}$ is fired horizontally at a stationary wooden block of mass $100\,\text{g}$. The pellet strikes the block with an impact velocity of $250\,\text{m s}^{-1}$. It becomes embedded in the block and does not come out. What is the speed of the block immediately after the pellet has become embedded?

Linear momentum and its conservation

A cupboard is fastened to a wall by means of a screw. Which force diagram shows the cupboard in equilibrium, with the weight $W$ of the cupboard, the force $S$ applied to the cupboard by the screw and the force $R$ applied to the cupboard by the wall?

Equilibrium of forces

A diving board with a length of $5.0\,\text{m}$ is hinged at one end and is supported $2.0\,\text{m}$ from that end by a spring of spring constant $10\,\text{kN m}^{-1}$. A child of mass $40\,\text{kg}$ stands at the free end of the board. How much extra compression does the spring undergo because of the child standing on the end of the board?

Turning effects of forces

The graph illustrates how the total resistive force on a train changes as its speed changes. One part of this force comes from wheel friction, and this stays constant. The remaining part is caused by wind resistance. At a speed of $200\,\text{km h}^{-1}$, what is the ratio $\frac{\text{wind resistance}}{\text{wheel friction}}$?

Momentum and Newton's laws of motion

In a water pumping system, the pump takes in $2.0\,\text{kW}$ of electrical power while lifting water. The system raises $16\,\text{kg}$ of water each second by a vertical distance of $7.0\,\text{m}$. What is the efficiency of the pumping system?

Gravitational potential energy and kinetic energy

A body moving at a speed of $20\,\text{m s}^{-1}$ has kinetic energy $E_k$. If its speed is raised to $80\,\text{m s}^{-1}$, what will its kinetic energy now be?

Gravitational potential energy and kinetic energy

An electrical generator is switched on at time zero. The graph shows the total electrical energy generated in the first $5\ \text{s}$. What is the greatest electrical power generated at any instant during these first $5\ \text{s}$?

Potential difference and power

Which unit corresponds to the coulomb?

SI units

Gold's density is $19.3\ \text{g cm}^{-3}$. A single gold atom may be treated as a cube with side length $2.6 \times 10^{-8}\ \text{cm}$. What mass does a gold atom have?

Density and pressure

In an experiment used to show Brownian motion, a clear container is filled with smoke particles floating in air. What is observed when the contents of the container are brightly lit and examined with a microscope?

Atoms, nuclei and radiation

A lift is held up by two steel cables, each with a length of $20\ \text{m}$. Each cable is made up of $100$ parallel steel wires, and each wire has a cross-sectional area of $3.2 \times 10^{-6}\ \text{m}^2$. The Young modulus of steel is $2.1 \times 10^{11}\ \text{N m}^{-2}$. How far does the lift move downwards when a man with mass $70\ \text{kg}$ gets into it?

Stress and strain

For a material stretched elastically within the limit of proportionality, what does the Young modulus equal?

Stress and strain

Electromagnetic waves from an unidentified source in space were observed to diffract strongly as they passed through openings of about $10^{-5}\ \text{m}$. Which kind of wave are they most likely to be?

Electromagnetic spectrum

The graph illustrates how the height of the water surface at a point in a harbour changes with time $t$ as waves move past the point. What values do $p$ and $q$ have?

Progressive waves

In each diagram, the three waves have identical amplitude and frequency, but they are out of phase. When combined, they produce a resultant wave. For which case is the resultant wave zero?

Interference

A stationary sound wave contains a sequence of nodes. The separation from the first node to the sixth node is $30.0\ \text{cm}$. Determine the wavelength of the sound wave.

Stationary waves

What does diffraction mean?

Diffraction

A student assembles apparatus to investigate double-slit interference of monochromatic light, as illustrated. Interference fringes appear on the screen. Which alteration would increase the spacing between neighbouring fringes?

Interference

Two coplanar vectors show two forces of the same magnitude. One points east and the other points north. In what direction must a single force act so that these two forces are balanced?

Scalars and vectors

A pair of charged, parallel metal plates creates an electric field. A charged particle travels from X to Y. Which graph shows how the force on the particle varies with distance from X along the line $XY$?

Potential difference and power

A small charge $q$ is positioned in the electric field produced by a large charge $Q$. Each charge experiences a force $F$. What is the electric field strength due to charge $Q$ at the location of charge $q$?

Potential difference and power

The current in a component falls evenly from $100\,\text{mA}$ to $20\,\text{mA}$ in $8.0\,\text{s}$. What charge passes in this interval?

Electric current

An electric current travels from a thick copper wire through a length of thinner copper wire and then into another thick copper wire, as shown. Which statement correctly describes the current and the speed of the electrons in the wires?

Electric current

An electrical device with a fixed resistance of $20\,\Omega$ is linked in series with a variable resistor and a battery whose electromotive force (e.m.f.) is $16\,\text{V}$ and whose internal resistance is negligible. What is the resistance of the variable resistor when the electrical device dissipates $4.0\,\text{W}$ of power?

Potential difference and power

A copper wire has a cylindrical shape and resistance $R$. What is the resistance of a copper wire with twice the length and twice the radius?

Resistance and resistivity

The diagram depicts the electric motor in a garden pump linked to a $24\,\text{V}$ power supply using an insulated two-core cable. The motor is not operating, so, in order to locate the fault, the negative terminal of a voltmeter is joined to the negative terminal of the power supply and the other end is connected in turn to terminals X and Y at the motor. Which row gives two readings and the correct conclusion?

Practical circuits

In the circuit illustrated, the thermistor’s resistance falls as the temperature rises. Which graph represents how the potential difference $V$ between points P and Q changes with Celsius temperature $\theta$?

Potential dividers

A $20\,\text{V}$ d.c. power supply is connected to a circuit made up of five resistors L, M, N, P and Q. Across L there is a potential drop of $7\,\text{V}$, and across N there is an additional potential drop of $4\,\text{V}$. What are the potential drops across M, P and Q?

Kirchhoff's laws

A nucleus of the nuclide $^{228}_{89}\text{Ac}$ undergoes decay by releasing a beta particle. This nuclear equation shows the process. $^{228}_{89}\text{Ac} \rightarrow ^{X}_{Y}\text{Th} + \beta$ Which combination of values for $X$ and $Y$ is correct?

Atoms, nuclei and radiation

The spring constant $k$ of a coiled wire spring is described by the formula $k = \dfrac{G r^4}{4 n R^3}$, where $r$ represents the radius of the wire, $n$ is the number of wire turns and $R$ is the radius of each turn of the wire. The quantity $G$ depends on the material that the wire is made from. What is a suitable unit for $G$?

SI units

Two $\alpha$-particles, each with equal energies, are deflected by a large nucleus. Which diagram shows their paths most accurately?

Atoms, nuclei and radiation

A voltmeter P, which is analogue and has not been calibrated, is connected in parallel with a second voltmeter Q that is known to be accurately calibrated. Readings from both meters are recorded over a range of potential difference (p.d.) values. The diagram displays the calibration graph obtained. From the graph, meter P is shown to have a zero error. The meter is then adjusted so that this zero error is removed. When the meter is recalibrated, the gradient of the calibration graph is found to remain unchanged. What is the new scale reading on meter P when it is used to measure a p.d. of $5.0\,\text{V}$?

Errors and uncertainties

A student wants to find the density $\rho$ of lead. She records the mass and diameter of a small lead sphere: mass $= (0.506 \pm 0.005)\,\text{g}$, diameter $= (2.20 \pm 0.02)\,\text{mm}$. What is the most reasonable estimate of the percentage uncertainty in her calculated value of $\rho$?

Errors and uncertainties

The graph illustrates how the velocity $v$ of a firework rocket varies with time $t$. At which point on the graph does the rocket experience the greatest acceleration?

Equations of motion

On one railway line, a train driver begins braking at a yellow signal, which is $1.0\,\text{km}$ before a red signal at which the train comes to rest. The train’s greatest deceleration is $0.20\,\text{m s}^{-2}$. If the deceleration is constant, what is the highest safe speed of the train at the yellow signal?

Equations of motion

A person is making a journey on a motorway covering a total of $200\,\text{km}$. The first $90\,\text{km}$ is completed at an average speed of $80\,\text{km h}^{-1}$. What average speed is needed for the remaining distance if the person is to arrive at the destination in a total time of $2$ hours $00$ minutes?

Non-uniform motion