May/June 2011

Decimal sub-multiples and multiples of units are shown by attaching a prefix to the unit. For instance, the prefix milli (m) means $10^{-3}$. Which row shows the sub-multiples or multiples represented by pico (p) and giga (G)?

SI units

A molecule of mass $m$ moving horizontally at velocity $u$ strikes a vertical wall perpendicular to its motion. It then bounces back horizontally with the same speed. What is the change in momentum?

Momentum and Newton's laws of motion

A cable car with weight $W$ is suspended in equilibrium from its cable at point P. As shown, the cable exerts tensions $T_1$ and $T_2$. Which diagram shows the forces acting at point P correctly?

Equilibrium of forces

The diagram illustrates four forces acting on a circular object. Which row states the resultant force and the resultant torque on the object?

Turning effects of forces

A metre rule that is uniform and has a mass of $100\,\text{g}$ is held up by a pivot at the $40\,\text{cm}$ mark and by a string attached at the $100\,\text{cm}$ mark. The string goes over a frictionless pulley and supports a mass of $20\,\text{g}$, as shown in the diagram. At which mark on the rule should a $50\,\text{g}$ mass be hung so that the rule is in balance?

Turning effects of forces

A steel sphere is released so that it falls vertically onto a horizontal metal plate. It reaches the plate with speed $u$, then moves away with speed $v$, and rises vertically to half of its starting height. Which expression gives the value of $\frac{v}{u}$?

Gravitational potential energy and kinetic energy

A $2.0\,\text{kg}$ block is let go from rest on an incline. It moves $7.0\,\text{m}$ along the slope and loses a vertical height of $3.0\,\text{m}$. The block is acted on by a frictional force of $5.0\,\text{N}$ parallel to the slope. What speed does the block have after descending this distance?

Energy conservation

A man has a mass of $80\,\text{kg}$. He fastens himself to one end of a rope that runs over a single fixed pulley. He then pulls the other end of the rope so that he rises with an average speed of $50\,\text{cm s}^{-1}$. What is the average useful power at which he is working?

Gravitational potential energy and kinetic energy

A body moving at a speed of $10\,\text{m s}^{-1}$ possesses kinetic energy of $1500\,\text{J}$. If the body’s speed is raised to $40\,\text{m s}^{-1}$, what kinetic energy does it now have?

Gravitational potential energy and kinetic energy

Which process does not need energy to be provided?

Energy conservation

$1.5\,\text{m}^3$ of water is combined with $0.50\,\text{m}^3$ of alcohol. Water has a density of $1000\,\text{kg m}^{-3}$ and alcohol has a density of $800\,\text{kg m}^{-3}$. Determine the density of the mixture when its volume is $2.0\,\text{m}^3$?

Density and pressure

Which definition is correct and uses quantities only, rather than units?

Physical quantities

A long, narrow metal wire is hung vertically from a fixed support. Masses are attached to its lower end. The load at the lower end is raised from zero and then lowered again until it returns to zero. The diagram illustrates the force-extension graph obtained. Where on the graph would the elastic limit be located?

Elastic and plastic behaviour

The Young modulus $E$ can be found from measurements taken when a wire is stretched. Which quantities should be measured in order to determine $E$?

Stress and strain

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 moment. 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 labelled correctly?

Progressive waves

Which statement concerning sound waves in air at a constant temperature is correct?

Transverse and longitudinal waves

A source of sound with constant power $P$ is placed in open space. The sound intensity $I$ at a distance $r$ from this source is given by $I = \dfrac{P}{4 \pi r^2}$. How does the amplitude $a$ of the oscillating air molecules depend on the distance $r$ from the source?

Progressive waves

Horn notes are produced by establishing a stationary wave in an air column. For the lowest note from a horn, a node occurs at the mouthpiece and an antinode occurs at the bell. The frequency of this note is $75\,\text{Hz}$. What are the frequencies of the next two notes above this one for this air column?

Stationary waves

Which electromagnetic wave phenomenon is required to account for the spectrum formed when white light is incident on a diffraction grating?

The diffraction grating

A diffraction grating containing $500$ lines per $\text{mm}$ is used to study diffraction of monochromatic light of wavelength $600\,\text{nm}$. The light is made to pass through a narrow slit, and the grating is positioned so that its lines are parallel to the slit. Light then travels through the slit and on through the grating. An observer looks at the slit through the grating at different angles, moving his head from X, parallel to the grating, through Y, opposite the slit, to Z, parallel to the grating on the other side. How many images of the slit are visible to him?

The diffraction grating

A potential difference is placed across two metal plates that are not parallel. Which diagram shows the electric field between the plates?

Potential difference and power

The diagram shows a charged particle moving towards a pair of charged parallel plates in a vacuum. Which row gives the horizontal and vertical components of its motion while it passes between the plates?

Equations of motion

A force of $5.0\,\text{N}$ acts on a ball towards due north, and a second force of $3.0\,\text{N}$ acts on it towards due east. What is the magnitude of the resultant force on the ball?

Scalars and vectors

A pair of parallel plates are separated by $25\ \text{mm}$, and the potential difference across them is $12\ \text{kV}$. What is the force on an electron when it is located in the uniform electric field between the plates?

Potential difference and power

A copper wire with cross-sectional area $2.0\ \text{mm}^2$ carries a current of $10\ \text{A}$. How many electrons pass through one chosen cross-section of the wire in 1 second?

Electric current

A battery is labelled $9.0\ \text{V}$. What is meant by this?

Potential difference and power

The graphs illustrate possible current-voltage ($I$-$V$) relationships for a filament lamp and for a semiconductor diode. Which row correctly gives the $I$-$V$ graphs for the lamp and the diode?

Resistance and resistivity

The resistance of a metal cube is determined by placing it between two parallel plates, as illustrated. The cube has volume $V$ and is formed from a material of resistivity $\rho$. The connections to the cube have negligible resistance. Which expression gives the electrical resistance of the metal cube between X and Y?

Resistance and resistivity

The diagram illustrates part of an electric circuit that carries current. The ammeter has negligible internal resistance. What reading does the ammeter show?

Practical circuits

Four resistors with the same value are connected as shown. How do the powers dissipated by the resistors change when resistor W is removed?

Potential difference and power

In the circuit diagram, XY is a uniform resistance wire of length $L$. $R_1$ and $R_2$ are unknown resistors. J is a sliding contact that connects the junction of $R_1$ and $R_2$ to points on XY via a small signal lamp S. To find the ratio $\dfrac{V_1}{V_2}$ of the potential differences across $R_1$ and $R_2$, a point on XY is located where the lamp does not light. This point is a distance $x$ from X. What is the value of the ratio $\dfrac{V_1}{V_2}$?

Practical circuits

The earliest artificial radioactive substance was formed by firing alpha-particles at aluminium, $^{27}_{13}\text{Al}$. In doing so, an unstable isotope of phosphorus, $^{30}_{15}\text{P}$, was generated. What was the other product of this reaction?

Atoms, nuclei and radiation

Uranium-238, $^{238}_{92}\text{U}$, undergoes $\alpha$-emission to form a daughter product, and that daughter product then undergoes $\beta$-emission to produce a grand-daughter product. What is the identity of the grand-daughter product?

Atoms, nuclei and radiation

The diagram displays a wave trace on a cathode-ray oscilloscope. The spacing between adjacent vertical and horizontal gridlines is $1.0\,\text{cm}$. The voltage scale is $4\,\text{V cm}^{-1}$ and the time scale is $5\,\text{ms cm}^{-1}$. What are the amplitude and period of the wave?

Progressive waves

Which statement concerning nuclei is correct?

Atoms, nuclei and radiation

The diagram illustrates an experiment for finding the speed of a small ball as it falls through a clear liquid inside a glass tube at constant speed. Two marks are shown on the tube. The upper mark is located at $115 \pm 1\,\text{mm}$ on the nearby rule, while the lower mark is at $385 \pm 1\,\text{mm}$. The ball reaches the upper mark at $1.50 \pm 0.02\,\text{s}$ and reaches the lower mark at $3.50 \pm 0.02\,\text{s}$. The ball's constant speed is found using $\frac{385 - 115}{3.50 - 1.50} = \frac{270}{2.00} = 135\,\text{mm s}^{-1}$. Which expression gives the fractional uncertainty in the speed value?

Errors and uncertainties

The graph illustrates how the acceleration of an object travelling in a straight line changes with time. Which graph shows how the velocity of the object varies with time?

Equations of motion

At time zero, a ball is released from rest. After $1.0\,\text{s}$, it makes an inelastic bounce off a horizontal surface and then rises again, reaching the highest point of its first rebound after $1.5\,\text{s}$. What is the ball’s total displacement from its starting position after $1.5\,\text{s}$?

Equations of motion

A body experiences a weight of $58.9\,\text{N}$ on the Earth. On the Moon, the acceleration of free fall is $1.64\,\text{m s}^{-2}$. What are the body’s weight and its mass when it is on the Moon?

Physical quantities

A body with mass $m$, travelling at velocity $v$, collides with an identical body that is at rest and remains attached to it. Which row gives the momentum and kinetic energy of the two bodies after the collision?

Linear momentum and its conservation

Stress has SI base units identical to those of

Stress and strain

A force $F$ acts on an object that is moving freely. At a particular moment, the object’s velocity is $v$ and its acceleration is $a$. Which of these quantities must point in the same direction?

Momentum and Newton's laws of motion

An object's momentum increases from $160\,\text{kg m s}^{-1}$ to $240\,\text{kg m s}^{-1}$ over $2\,\text{s}$. What is the mean resultant force acting on the object during this interval?

Momentum and Newton's laws of motion

A car moves with acceleration along a straight line. A graph showing the car’s momentum against time is drawn. What is evaluated by calculating the gradient of the graph at a specific time?

Momentum and Newton's laws of motion

The diagram depicts particle P moving at speed $v$ and just about to strike a stationary particle Q with the same mass. The collision is perfectly elastic. Which statement gives the motion of P and of Q immediately after the collision?

Linear momentum and its conservation

A stone is launched horizontally in a vacuum and follows the path illustrated. X is located on this path. Through X, XV and XH are the vertical and horizontal lines respectively. XT is the tangent to the path at X. In which directions do forces act on the stone at X?

Momentum and Newton's laws of motion

The diagrams each depict a pair of equal forces acting on a metre rule. Which diagram shows forces that produce a couple and zero resultant force?

Turning effects of forces

A uniform rod XY, with weight $10.0\,\text{N}$, is attached by a free hinge to a wall at X. As shown, it remains horizontal because of a force $F$ applied at Y at an angle of $30^\circ$ to the horizontal. What is the value of $F$?

Turning effects of forces

The diagram depicts two fixed pins, Y and Z. A length of elastic is stretched from Y to Z and passes around pin X, which is attached to a trolley. X is positioned at the midpoint of the elastic, and the trolley is to be driven in direction P at right angles to YZ. The tension in the elastic is $4\,\text{N}$. What force accelerates the trolley in direction P when the trolley is released?

Momentum and Newton's laws of motion

An electric motor delivers $120\,\text{W}$ of useful mechanical output power. The motor has an efficiency of $60\%$. Which row is correct?

Potential difference and power

A hammer that has $10\,\text{J}$ of kinetic energy strikes a nail and drives it $5.0\,\text{mm}$ into a plank. After the collision, both the hammer and the nail are brought to rest. What is the average force acting on the nail as it moves through the $5.0\,\text{mm}$?

Energy conservation

To verify the calculations, the units are substituted into the equations below alongside the numbers. Which equation has to be incorrect?

SI units

The figure depicts two vessels, P and Q, each having sides that are tilted at $45^{\circ}$. As illustrated, vessel P widens upwards while vessel Q narrows upwards. Each vessel contains a liquid, and the liquids are at the same depth. The liquid in vessel P has twice the density of the liquid in vessel Q. Find the ratio $\dfrac{\text{pressure due to the liquid on the base of P}}{\text{pressure due to the liquid on the base of Q}}$?

Density and pressure

Two solid substances P and Q consist of atoms with masses $M_P$ and $M_Q$ respectively. They contain $n_P$ and $n_Q$ atoms in each unit volume. The density of P is higher than the density of Q. Which statement must be true?

Density and pressure

The table gives a summary of several descriptions of evaporation. Which row in the table is correct?

Energy conservation

The way a wire responds when it is stretched can be explained using the Young modulus $E$ of the wire’s material and the force per unit extension $k$ of the wire. For a wire with length $L$ and cross-sectional area $A$, what relationship links $E$ and $k$?

Stress and strain

The diagram illustrates the structure of part of a mattress. The manufacturer wants to produce a softer mattress, meaning one that will compress more under the same load. Which change would not produce the required effect?

Stress and strain

What order of magnitude do the frequencies of electromagnetic waves in the visible spectrum have?

Electromagnetic spectrum

A transverse progressive wave is produced on a string. The graph illustrates how the displacement of one point on this string changes 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

Any wave that can be polarised must be

Polarisation

Under what circumstances does diffraction take place?

Diffraction

The diagrams illustrate how the apparatus is set up for a Young’s slits experiment, together with part of the pattern produced on the screen, with a ruler shown beside it. What wavelength does the light have?

Interference

When making reasonable estimates of physical quantities, which statement is incorrect?

Errors and uncertainties

The diagram depicts two parallel metal plates linked to a d.c. power supply via a resistor. A uniform electric field exists in the space between the plates. Which change would lead to a decrease in the electric field strength?

Potential difference and power

In each electric field diagram, a positively charged particle is transferred from X to Y. In which diagram does the particle feel a repulsive force that gets larger?

Potential difference and power

What term is used for the electric potential difference between two points in a wire carrying a current?

Potential difference and power

A soft, electrically-conducting cylindrical sample has resistance $R$. It is rolled out so that its length becomes twice as great, while its volume remains constant. What is its new resistance?

Resistance and resistivity

An e.m.f. source $E$ has a fixed internal resistance $r$ and is connected to an external variable resistor of resistance $R$. As $R$ is raised from a value smaller than $r$ to a value larger than $r$, which statement is correct?

Potential difference and power

Which graph most accurately shows how the current $I$ through a thermistor varies with the potential difference $V$ across it?

Resistance and resistivity

Railway safety is improved by using a number of electrical switches. In the diagram, switches P, Q, R, S and T control the current through a green lamp. Which row prevents the green lamp from lighting?

Practical circuits

The diagram depicts a fixed resistor and a light-dependent resistor (LDR) connected in series to a constant low-voltage supply. When the LDR is in the dark, the fixed resistor and the LDR have equal resistance values. Light is directed onto the LDR. What happens to the potential differences across the two components?

Potential dividers

The diagram illustrates a d.c. circuit. What is the resistance between points $P$ and $Q$ caused by the resistance network?

Resistance and resistivity

The uranium nucleus $^{238}_{92}\text{U}$ undergoes $\alpha$-decay and forms nucleus X. Nucleus X then undergoes $\beta$-decay and forms nucleus Y. For nucleus Y, what are the proton number and nucleon number?

Atoms, nuclei and radiation

How much uncertainty there is in the momentum of a trolley moving between points X and Y depends on which measuring devices are chosen. Readings for the same trolley taken with different instruments are given below. 1 distance between X and Y measured with a metre rule with cm divisions $= 0.55\,\text{m}$ 2 distance between X and Y measured with a metre rule with mm divisions $= 0.547\,\text{m}$ 3 timings taken with a wristwatch reading to the nearest $0.5\,\text{s}$ at X $= 0.0\,\text{s}$ and at Y $= 4.5\,\text{s}$ 4 timings taken with light gates reading to the nearest $0.1\,\text{s}$ at X $= 0.0\,\text{s}$ and at Y $= 4.3\,\text{s}$ 5 mass of trolley measured with a balance reading to the nearest g $= 6.4 \times 10^{-2}\,\text{kg}$ 6 mass of trolley measured with a balance reading to the nearest $10\,\text{g} = 6 \times 10^{-2}\,\text{kg}$ Which measurements, one for each quantity measured, produce the smallest uncertainty in the trolley's momentum value?

Errors and uncertainties

Radon-220 is radioactive and undergoes decay to polonium-216 by emitting an $\alpha$-particle. The decay equation is shown below. $^{220}_{86}\text{Rn} \rightarrow ^{216}_{84}\text{Po} + ^{4}_{2}\text{He}$. How many neutrons are present in the radon and polonium nuclei?

Atoms, nuclei and radiation

The time-base of a cathode-ray oscilloscope is adjusted to $6\,\text{ms}\,\text{cm}^{-1}$. A trace containing two pulses is shown in the diagram. What is the time interval separating the two pulses?

Practical circuits

A bullet is launched horizontally at speed $v$ from a rifle. During a brief time $t$ after it leaves the rifle, gravity is the only force acting on its motion. The acceleration of free fall is $g$. Which expression gives the horizontal distance travelled in time $t$ divided by the vertical distance travelled in time $t$?

Equations of motion

A particle’s motion is represented by the velocity-time graph. The displacement of the particle is taken to be zero at $t = 0$. Point Q marks a point on its path. Which row in the table is correct?

Non-uniform motion

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

Equations of motion

A small glider travels along a smooth horizontal air track, as shown below. There is a perfectly elastic buffer at each end of the air track. Which graph shows how the velocity v of the glider changes with time t as it moves between the two buffers?

Equations of motion

A force of $5.0\,\text{N}$ acts on a ball in the due north direction, while a second force of $3.0\,\text{N}$ acts on it due east. What is the magnitude of the resultant force on the ball?

Scalars and vectors

A body of mass $m$, travelling with velocity $v$, collides with another body of the same mass that is at rest and then remains attached to it. Which row shows the momentum and kinetic energy of the two bodies after the collision?

Linear momentum and its conservation

The diagram illustrates four forces acting on a circular object. Which row gives the resultant force and resultant torque on the object?

Turning effects of forces

A uniform metre rule with mass $100\,\text{ g}$ is held up by a pivot at the $40\,\text{ cm}$ mark and by a string attached at the $100\,\text{ cm}$ mark. The string goes over a frictionless pulley and supports a mass of $20\,\text{ g}$, as shown in the diagram. At what mark on the rule should a $50\,\text{ g}$ mass be hung so that the rule is in balance?

Turning effects of forces

A cable car with weight $W$ is in equilibrium, suspended from its cable at point $P$. The cable exerts tensions $T_1$ and $T_2$ as shown. Which diagram correctly shows the forces acting at point $P$?

Equilibrium of forces

A steel sphere is released so that it falls vertically onto a horizontal metal plate. It strikes the plate with speed $u$, then departs from it with speed $v$, and rises vertically again to half of its starting height. Which expression represents $\frac{v}{u}$?

Gravitational potential energy and kinetic energy

A block of mass $2.0\,\text{kg}$ is set free from rest on a slope. It moves $7.0\,\text{m}$ along the slope and drops through a vertical height of $3.0\,\text{m}$. A frictional force of $5.0\,\text{N}$ acts parallel to the slope. Determine the speed of the block after it has fallen this distance?

Gravitational potential energy and kinetic energy

An object moving at a speed of $10\,\text{m s}^{-1}$ has a kinetic energy of $1500\,\text{J}$. When the speed of the object is raised to $40\,\text{m s}^{-1}$, what is its new kinetic energy?

Gravitational potential energy and kinetic energy

A man of mass $80\,\text{kg}$ attaches himself to one end of a rope that goes over a single fixed pulley. He pulls the free end of the rope so that he rises with an average speed of $50\,\text{cm s}^{-1}$. What is the average useful power at which he is working?

Energy conservation

Which process does not need energy to be provided?

Energy conservation

$1.5\,\text{m}^3$ of water is combined with $0.50\,\text{m}^3$ of alcohol. The density of water is $1000\,\text{kg m}^{-3}$ and the density of alcohol is $800\,\text{kg m}^{-3}$. What is the density of the mixture with volume $2.0\,\text{m}^3$?

Density and pressure

Prefixes are added to units to show decimal sub-multiples and multiples. For example, milli (m) stands for $10^{-3}$. Which row shows the sub-multiples or multiples represented by pico (p) and giga (G)?

SI units

The Young modulus $E$ may be found using measurements taken while a wire is under tension. Which quantities need to be measured in order to determine $E$?

Stress and strain

A long, thin metal wire is hung vertically from a fixed support. Masses are attached to its lower end. The load at the lower end is raised from zero and then reduced again to zero. The diagram shows the force-extension graph that is obtained. Where on the graph is the elastic limit located?

Elastic and plastic behaviour

A source of sound with constant power $P$ is placed in open space. The sound intensity $I$ at a distance $r$ from the source is given by $I = \frac{P}{4\pi r^2}$. How does the amplitude $a$ of the vibrating air molecules depend on the distance $r$ from the source?

Progressive waves

The four graphs depict a progressive wave on a stretched string. Graphs A and B illustrate how displacement $d$ changes with distance $x$ along the string at a single moment. Graphs C and D illustrate how displacement $d$ changes with time $t$ at one fixed value of $x$. The graph labels 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

Which statement regarding sound waves in air when the temperature remains constant is correct?

Transverse and longitudinal waves

Which electromagnetic wave phenomenon is required to account for the spectrum formed when white light is incident on a diffraction grating?

The diffraction grating

A diffraction grating that has 500 lines per mm is employed to study the diffraction of monochromatic light with wavelength $600\,\text{nm}$. The light is first sent through a narrow slit, and the grating is positioned so that its lines run parallel to the slit. The light then travels through the slit and afterwards through the grating. An observer looks at the slit through the grating at a range of angles, shifting his head from X parallel to the grating, via Y, opposite the slit, to Z parallel to the grating on the far side. How many images of the slit does he see?

The diffraction grating

The fundamental idea behind producing notes on a horn is to create a stationary wave within an air column. In the lowest note that a horn can produce, a node appears at the mouthpiece while an antinode appears at the bell. The frequency of this note is $75\,\text{Hz}$. What are the frequencies of the next two higher notes for this air column?

Stationary waves

A potential difference of $12\,\text{kV}$ is applied across two parallel plates separated by a gap of $25\,\text{mm}$. What force acts on an electron located in the uniform electric field between the plates?

Potential difference and power

A potential difference is applied across two metal plates that are not parallel. Which diagram represents the electric field between the plates?

Potential difference and power

Which definition is correct and is expressed using quantities instead of units?

Physical quantities

The diagram illustrates a charged particle as it moves towards a pair of charged parallel plates in a vacuum. Which row gives the horizontal and vertical components of its motion as it passes between the plates?

Equations of motion

A battery is labelled $9.0\,$V. What is the meaning of this?

Potential difference and power

A copper wire with cross-sectional area $2.0\,\text{mm}^2$ carries a current of $10\,\text{A}$. How many electrons pass across a particular cross-section of the wire in one second?

Electric current

Four resistors with identical resistance are connected as shown. How will the power dissipated by the resistors change when resistor W is removed?

Kirchhoff's laws

The graphs illustrate possible current-voltage ($I$-$V$) characteristics for a filament lamp and for a semiconductor diode. Which row most accurately states the correct $I$-$V$ graphs for the lamp and the diode?

Resistance and resistivity

The resistance of a metal cube is determined by putting it between two parallel plates, as illustrated. The cube has volume $V$ and is made from a material of resistivity $\rho$. The connections to the cube have negligible resistance. Which expression gives the electrical resistance of the metal cube between X and Y?

Resistance and resistivity

In the circuit diagram shown, XY is a length $L$ of uniform resistance wire. $R_1$ 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 small signal lamp S. To find the ratio $\frac{V_1}{V_2}$ of the potential differences across $R_1$ and $R_2$, a point is located on XY where the lamp is not lit. This point lies a distance $x$ from X. What is the value of the ratio $\frac{V_1}{V_2}$?

Potential dividers

The diagram illustrates a section of a current-carrying circuit. The ammeter has negligible internal resistance. What reading does the ammeter show?

Practical circuits

Which of the following statements about nuclei is correct?

Atoms, nuclei and radiation

The earliest artificial radioactive substance was produced by striking aluminium, $^{27}_{13}\text{Al}$, with $\alpha$-particles. As a result, an unstable phosphorus isotope, $^{30}_{15}\text{P}$, was formed. What was the other product of this reaction?

Atoms, nuclei and radiation

The diagram illustrates an experiment for measuring the speed of a small ball as it falls through a clear liquid inside a glass tube at constant speed. Two marks are drawn on the tube. The upper mark is at $115 \pm 1\,\text{mm}$ on the nearby rule, while the lower mark is at $385 \pm 1\,\text{mm}$. The ball crosses the upper mark at $1.50 \pm 0.02\,\text{s}$ and crosses the lower mark at $3.50 \pm 0.02\,\text{s}$. The constant speed of the ball is found using $\dfrac{385 - 115}{3.50 - 1.50} = \dfrac{270}{2.00} = 135\,\text{mm s}^{-1}$. Which expression is used to calculate the fractional uncertainty in this speed value?

Errors and uncertainties

A Uranium-238 nucleus, $^{238}_{92}\text{U}$, undergoes $\alpha$-emission to form a daughter product, which then undergoes $\beta$-emission to produce a grand-daughter product. What is the grand-daughter product?

Atoms, nuclei and radiation

The diagram displays a trace of a wave on a cathode-ray oscilloscope. The vertical and horizontal gridlines are spaced by $1.0\,\text{cm}$. The voltage scaling is $4\,\text{V cm}^{-1}$ and the time scaling is $5\,\text{ms cm}^{-1}$. Calculate the amplitude and period of the wave.

Progressive waves

An object has a weight of $58.9\,\text{N}$ on Earth. On the Moon, the acceleration of free fall is $1.64\,\text{m s}^{-2}$. What are the object's weight and mass on the Moon?

Physical quantities

The graph indicates how an object’s acceleration, while travelling along a straight line, changes with time. Which graph shows how the object’s velocity changes with time?

Equations of motion

A ball is let go from rest at time zero. After $1.0\,\text{ s}$ it strikes a horizontal surface inelastically and rebounds, reaching the highest point of its first bounce after $1.5\,\text{ s}$. What is the ball's total displacement from its starting position after $1.5\,\text{ s}$?

Equations of motion

A molecule of mass $m$ moving horizontally at speed $u$ strikes a vertical wall perpendicular to its direction of motion. It then bounces back horizontally with the same speed. What is its change in momentum?

Momentum and Newton's laws of motion