Oct/Nov 2012

Which SI base unit(s) are used to express weight?

SI units

A golf ball is struck with the same force and in the same direction on the Earth and on the Moon. Which diagram shows the best representation of the shapes of the paths followed by the golf ball?

Equations of motion

An object moving with velocity $v$ collides with a wall and then rebounds, as illustrated. Which quantity of the object is not conserved?

Linear momentum and its conservation

A particle $X$ is moving at speed $v$ and makes a perfectly elastic collision with an identical particle $Y$ that is at rest. After the collision, what are the speed and direction of motion of each particle?

Linear momentum and its conservation

A $2.0\,\text{kg}$ mass is at rest on a frictionless surface. It is connected to a $1.0\,\text{kg}$ mass by a light, thin string that runs over a frictionless pulley. The $1.0\,\text{kg}$ mass is let go and accelerates downward. What is the speed of the $2.0\,\text{kg}$ mass when the $1.0\,\text{kg}$ mass reaches the floor, after descending $0.50\,\text{m}$?

Momentum and Newton's laws of motion

A lead pellet is fired straight upward into a clay block, which is at rest at the instant of collision but can move upward without restriction after the impact. The pellet strikes the block with an initial velocity of $200\,\text{m s}^{-1}$. It becomes lodged in the block and does not pass back out. To what height above its starting point does the block climb? (Mass of pellet $= 5.0\,\text{g}$; mass of clay block $= 95\,\text{g}$.)

Linear momentum and its conservation

The diagram illustrates an experiment for determining the force acting on a ball due to a horizontal stream of air. The ball hangs from a light string and has a weight of $0.15\,\text{N}$. The string is deflected by $30^{\circ}$ from the vertical. What is the force on the ball caused by the air flow?

Equilibrium of forces

A student puts a $30\,\text{cm}$ ruler on a fulcrum positioned at the $15\,\text{cm}$ mark. She next adds a $50\,\text{g}$ mass at the $23\,\text{cm}$ mark and a $20\,\text{g}$ mass at the $11\,\text{cm}$ mark, as shown. Which mass should she add at the $7\,\text{cm}$ mark in order to make the ruler balance again?

Turning effects of forces

A sledge moves down a slope with constant velocity. The three forces acting on the sledge are the normal contact force $C$, the weight $W$ and a frictional force $F$ of constant size. Which diagram shows these forces acting on the sledge?

Equilibrium of forces

The kinetic energy of a particle is multiplied by a factor of $4$. By what factor does its speed increase?

Gravitational potential energy and kinetic energy

The piston in a gas supply pump has a cross-sectional area of $600\,\text{cm}^2$, and in one stroke it travels $40\,\text{cm}$. The pump pushes the gas against a constant pressure of $5000\,\text{Pa}$. What amount of work is carried out by the piston in one stroke?

Density and pressure

P and Q are vectors drawn to scale. Which diagram shows the vector $(P - Q)$?

Scalars and vectors

A train engine increases the speed of a train with total mass $800$ tonnes ($1$ tonne $= 1000\,\text{kg}$) from rest until it reaches $50\,\text{m s}^{-1}$. What amount of work has to be done on the train for it to attain this speed?

Gravitational potential energy and kinetic energy

Water from a reservoir flows to the turbine in a hydroelectric system at a rate of $500\,\text{kg s}^{-1}$. The reservoir lies $300\,\text{m}$ above the turbine level. The electrical output from the generator driven by the turbine is $200\,\text{A}$ at a potential difference of $6000\,\text{V}$. What is the efficiency of the system?

Gravitational potential energy and kinetic energy

Which row correctly shows how closely together the molecules are, how they are arranged and how they move in water and in ice when both are at a temperature of $0^{\circ}\text{C}$?

Density and pressure

The three springs are placed one above another in a vertical line, as illustrated. Springs $P$ and $Q$ are the same and each has spring constant $k$. Spring $R$ has spring constant $3k$. When a force $W$ is applied as shown, by how much does the total length of the arrangement increase?

Elastic and plastic behaviour

The diagram presents the stress-strain graph for two wires X and Y made from different materials, drawn up to their breaking points. The two wires start with identical dimensions. Which statement is not correct?

Elastic and plastic behaviour

A steel wire and a brass wire are connected in series and suspended vertically, with the steel wire fixed to a point on the ceiling. The steel wire is twice the length of the brass wire and has a diameter that is half as large. A large mass is suspended from the lower end of the brass wire so that both wires undergo elastic extension. The Young modulus of steel is $2.0 \times 10^{11}\,\text{Pa}$ and the Young modulus of brass is $1.0 \times 10^{11}\,\text{Pa}$. What is the ratio of the extension of the steel to the extension of the brass?

Stress and strain

The diagram presents a graph of displacement plotted against time for a sound wave. The sound intensity is reduced to half. Which graph represents the displacement of this sound wave?

Progressive waves

Which objects do not travel at the speed of light in a vacuum?

Transverse and longitudinal waves

An organ makes notes by sending air through a collection of pipes that are open at one end and closed at the other. What is the lowest frequency of sound generated by a pipe with length $10\,\text{m}$? (The speed of sound in the pipe is $320\,\text{m s}^{-1}$.)

Stationary waves

A beam of monochromatic light is incident on a diffraction grating, as illustrated. Which diagram shows every possible direction of the light after it has passed through the grating that produces maximum intensity?

The diffraction grating

About what temperature is a red-hot ring on an electric cooker?

Electromagnetic spectrum

An electron starts from rest in a uniform electric field. Which graph represents how the electron’s velocity varies with time?

Equations of motion

A charged particle is located in the electric field between two horizontal metal plates that are connected to a source providing a constant potential difference, as shown. The electric field exerts a force $F$ on the particle. The distance between the plates is doubled. What will the new force on the particle be?

Potential difference and power

In a circuit, the potential difference across points X and Y is $20\text{ V}$. The charge carriers take $15\text{ s}$ to travel from X to Y. During this interval, their energy changes by $12\text{ J}$. Determine the current between X and Y?

Potential difference and power

A wire with a cylindrical shape is $10\text{ m}$ long and has a diameter of $2.0\text{ mm}$. Its resistance is $0.050\,\Omega$. Which material is the wire made from?

Resistance and resistivity

The $I$-$V$ characteristics for two electrical components P and Q are shown below. Which of the following statements is correct?

Resistance and resistivity

Within a fire alarm system, thermistor T has a resistance of $2000\,\Omega$ at room temperature. As the temperature rises, its resistance falls. The alarm operates when the potential difference between X and Y becomes $4.5\text{ V}$.\n\nWhat is the resistance of the thermistor at the point when the alarm is triggered?

Potential dividers

A circuit of electrical components is arranged across a battery with negligible internal resistance, as illustrated. The resistance of the variable resistor is then increased. How do the ammeter reading and the voltmeter reading change?

Practical circuits

The diagram depicts a potentiometer circuit. The contact T is positioned on the wire and then slid along it until the galvanometer gives a zero reading. The length $XT$ is then recorded. To work out the potential difference per unit length of the wire $XY$, what other value has to be known?

Potential dividers

A group of students modelled radioactive decay with dice. Following each throw, any dice landing on a ‘6’ were taken away. The graph shows the findings. What might the spread of points around the best-fit curve indicate for real radioactive decay?

Atoms, nuclei and radiation

Which of the following statements about alpha, beta and gamma radiation is correct?

Atoms, nuclei and radiation

Which list includes only scalar quantities?

Scalars and vectors

In a radioactive decay chain, three decays occur one after another, and each one leads to the emission of a particle. The first decay leads to the emission of a $\beta$-particle. The second decay leads to the emission of an $\alpha$-particle. The third decay leads to the emission of another $\beta$-particle. Nuclides P and S are being compared. Which statement is true?

Atoms, nuclei and radiation

The density of the material in a coil made of thin wire is to be determined. Which collection of instruments would be used to carry this out most accurately?

Errors and uncertainties

A quantity $X$ depends on temperature $\theta$ as shown. $\theta$ is found from the matching values of $X$ by using this graph. $X$ is measured with a percentage uncertainty of $\pm 1\%$ of its value at all temperatures. Which statement about the uncertainty in $\theta$ is correct?

Errors and uncertainties

A measurement of a physical quantity can be affected by random errors and by systematic errors. Which statement is correct?

Errors and uncertainties

The velocity of an electric car varies as illustrated. What is the car’s acceleration?

Equations of motion

A ball is projected vertically upwards into the air. Ignoring air resistance, which property of the ball can never become zero at any stage of its motion?

Equations of motion

Which physical quantity has base units identical to those of momentum?

Momentum and Newton's laws of motion

The dotted line indicates the route of a competitor during a ski-jumping event. If air resistance is ignored, which graph best shows how his speed $v$ changes with the horizontal distance $x$ travelled from the beginning of his jump at $P$ until he lands at $Q$?

Equations of motion

The car’s velocity varies as shown. What is the car’s acceleration?

Equations of motion

A ball with mass $0.5\,\text{kg}$ is hurled at a wall at a speed of $12\,\text{m s}^{-1}$. After rebounding, it moves back at $8\,\text{m s}^{-1}$. The contact time is $0.10\,\text{s}$. Determine the average force on the ball caused by the collision.

Momentum and Newton's laws of motion

Two identical spheres, each perfectly elastic, have equal mass $m$. They move towards one another at the same speed $v$ across a horizontal surface with no friction. Which statement correctly describes the total kinetic energy of the spheres?

Linear momentum and its conservation

A $1.2\,\text{kg}$ mass is held up by a person’s hand and two newton-meters, as shown. After the person’s hand is taken away, what is the mass’s initial vertical acceleration?

Momentum and Newton's laws of motion

A lorry with a mass of $20\,000\,\text{kg}$ experiences a constant resultant force $F$. Its speed increases from $6.0\,\text{m s}^{-1}$ to $30.0\,\text{m s}^{-1}$ over $300\,\text{s}$. Determine the lorry’s change in momentum and the value of $F$?

Momentum and Newton's laws of motion

A body at rest is floating in water. Which statement about the forces acting on the body is correct?

Density and pressure

A rigid, uniform beam is hinged horizontally at its centre. Various vertical forces are exerted at different points along the beam. In which diagram is the beam in equilibrium?

Turning effects of forces

A picture hanging on a wall is held in place by a wire that passes over a nail. The mass of the picture is $4.2\text{ kg}$. What is the tension in the wire supporting it?

Equilibrium of forces

A piston in a gas supply pump has an area of $500\text{ cm}^2$ and, in one stroke, it travels $30\text{ cm}$. The pump pushes the gas against a constant pressure of $4000\text{ Pa}$. How much work is done by the piston in one stroke?

Density and pressure

Vectors $\vec{P}$ and $\vec{Q}$ have been drawn to scale. Which diagram shows the vector $(\vec{P} + \vec{Q})$?

Scalars and vectors

A train with a total mass of $1200$ tonnes $(1\text{ tonne} = 1000\text{ kg})$ is brought from rest up to a speed of $75\text{ m s}^{-1}$ by a railway engine. What amount of useful work has to be done on the train for it to reach this speed?

Gravitational potential energy and kinetic energy

A crane is used to raise containers from a ship. One container has a mass of $14\,000\text{ kg}$ and is being moved upwards at a speed of $3.2\text{ m s}^{-1}$. The electric motor that provides the power for lifting the container takes a current of $240\text{ A}$ at a potential difference of $2200\text{ V}$. Calculate the efficiency of the system.

Potential difference and power

Coal is delivered to a power station by trains. The table below shows quantities linked to how the power station operates. Power station output $P$ (W) Number of trains per day $N$ Mass of coal on one train $M$ (kg) Energy from $1\text{ kg}$ of coal $J$ (J) Number of seconds in one day $S$ Which expression shows the efficiency of the power station?

Energy conservation

Which row correctly shows how closely the molecules are packed and how they move in water and in ice when both are at a temperature of $0\degree\text{C}$?

Density and pressure

Which row correctly describes how atoms are arranged in the four types of material?

Atoms, nuclei and radiation

What evidence supports the conclusion that molecules move randomly?

Atoms, nuclei and radiation

The diagram presents the force-extension graphs for two materials with identical dimensions, each loaded until fracture. Which statement describes how the materials behave?

Elastic and plastic behaviour

Wires X and Y are each made from different metals and have unlike dimensions. The Young modulus of wire X is twice the Young modulus of wire Y. Wire X has a diameter that is half the diameter of wire Y. The two wires are stretched so that they have the same strain, and both satisfy Hooke’s law. What is the ratio $\dfrac{\text{tension in wire X}}{\text{tension in wire Y}}$?

Stress and strain

The diagram depicts two identical loudspeakers, both driven in phase by a shared audio-frequency source. As a student walks along line XY, he observes changes in the sound loudness. The sound is heard in alternating loud and quiet regions, as shown on the diagram. How may the separation between the loud regions be reduced?

Interference

A glass tube lies horizontally and is sealed at one end, with a thin layer of dust resting on its underside inside the tube. A loudspeaker is positioned close to the open end of the tube and sends out sound. The sound frequency is changed, and at one particular frequency a stationary wave is produced within the tube, causing the dust to collect into small piles. The separation between four heaps of dust is $30\ \text{cm}$. The speed of sound in the tube is $330\ \text{m s}^{-1}$. What frequency is the sound from the loudspeaker?

Stationary waves

During a 100 m race, what is the Olympic athlete’s approximate kinetic energy when they are running at maximum speed?

Gravitational potential energy and kinetic energy

Monochromatic light with wavelength $690\ \text{nm}$ is incident on a diffraction grating having $300\ \text{lines mm}^{-1}$, creating a sequence of maxima on a screen. What is the maximum number of maxima that may be seen?

The diffraction grating

The diagram shows the display of an electromagnetic wave on a cathode-ray oscilloscope. The time base setting is $0.20\ \mu\text{s cm}^{-1}$. Which statement is correct?

Progressive waves

A charged particle travels through a uniform electric field between two parallel metal plates. To calculate the force on the particle caused by the electric field, which quantity is not needed?

Potential difference and power

A single proton moves into a uniform electric field between two parallel charged plates with a steady horizontal velocity. In the diagram, B shows the route followed by the proton. Which route is followed by a helium nucleus that enters the electric field at the same point and with the same velocity as the proton?

Momentum and Newton's laws of motion

The graph illustrates how resistance $R$ changes as the length $l$ of two wires X and Y, both made from the same material, varies. What is shown by the graph?

Resistance and resistivity

A cell with internal resistance $2.0\,\Omega$ and electromotive force (e.m.f.) $1.5\,\text{V}$ is connected to a resistor whose resistance is $3.0\,\Omega$. What is the potential difference across the $3.0\,\Omega$ resistor?

Potential difference and power

A $100\,\Omega$ resistor carries a current whose direction and magnitude vary with time, as shown. What is the average power dissipated in the resistor?

Potential difference and power

The current shown by the ammeter in the circuit below is $I$. A different circuit, which has the same voltage supply, two switches, an ammeter and two resistors, each with resistance $R$, is shown. Which row is incorrect?

Practical circuits

A light-dependent resistor $R$ has a resistance of about $1\,\text{M}\Omega$ in darkness and about $1\,\text{k}\Omega$ when it is lit. It is arranged in series with a $5\,\text{k}\Omega$ resistor and a $1.5\,\text{V}$ cell of negligible internal resistance. The light-dependent resistor is exposed, in an otherwise dark room, to a flashing light. Which graph best indicates how the potential difference $V$ across $R$ changes with time $t$?

Potential dividers

A material includes a radioactive isotope that decays only through the emission of $\alpha$-particles at a rate of $100\,\text{s}^{-1}$. Which statement about this material is correct?

Atoms, nuclei and radiation

Physical quantities may be grouped into vectors or scalars. Which pair of quantities is made up of two vectors?

Scalars and vectors

A stable nucleus may be converted into another nucleus by being bombarded with an energetic $\alpha$-particle. $^{23}_{11}\text{Na}$ is bombarded with an energetic $\alpha$-particle. What could be the products of this nuclear reaction?

Atoms, nuclei and radiation

A student is given a reel of wire with diameter smaller than $0.2\ \text{mm}$ and has to determine the metal’s density. Which pair of instruments would be most appropriate for measuring the volume of the wire?

Physical quantities

Variables $x$ and $y$ are connected by the equation $y = p - qx$ where $p$ and $q$ are constants. The values of $x$ and $y$ are obtained experimentally. The data include a systematic error. Which graph most accurately shows these results?

Errors and uncertainties

The speed of a car is found using measurements of the distance travelled and the time taken. The distance is recorded as $200\ \text{m}$, with an uncertainty of $\pm 2\ \text{m}$. The time is recorded as $10.0\ \text{s}$, with an uncertainty of $\pm 0.2\ \text{s}$. What is the percentage uncertainty in the calculated speed?

Errors and uncertainties

A museum of science plans an experiment to demonstrate a feather falling through a vertical glass vacuum tube. The fall time from rest should be about $0.5\ \text{s}$. How long should the tube be?

Equations of motion

A graph showing velocity plotted against time for an object travelling in a straight line is given. Which graph represents displacement against time for the same object?

Equations of motion

The units for all physical quantities can be written in terms of SI base units. Which pair contains quantities with identical base units?

SI units

A mass attached to the end of a spring oscillates up and down, as illustrated, after it is released at time $t = 0$. Which graph shows the way the velocity changes with time?

Equations of motion

The diagram illustrates two spherical masses moving directly towards one another at the same speed $u$. One has mass $m$ and the other has mass $2m$. Which diagram, representing the situation after the collision, is inconsistent with the principle of conservation of momentum?

Linear momentum and its conservation

A molecule with mass $m$ is moving at speed $v$ and strikes a wall at right angles to the wall. The collision is elastic. What changes occur in the molecule’s kinetic energy and momentum as a result of the collision?

Momentum and Newton's laws of motion

IKAROS satellite has a mass of $320\,\text{kg}$ and travels through space with a solar sail whose area is $20\,\text{m}^2$. The mean pressure of the solar wind is $1.0 \times 10^{-5}\,\text{N m}^{-2}$. What acceleration does the solar wind produce on the satellite?

Momentum and Newton's laws of motion

The graph plots the momentum of a cyclist over an interval of $8.0\,\text{s}$. At time $4.0\,\text{s}$, she applies the brakes. What is the resultant force on the cyclist during the time when the brakes are applied?

Momentum and Newton's laws of motion

A hailstone, at first at rest at the bottom of a cloud, descends vertically towards the Earth. The diagram shows the sizes and directions of the forces acting on the hailstone as it begins to fall. Which diagram shows the sizes and directions of these forces when the hailstone reaches terminal (constant) speed in air (of uniform density)?

Equilibrium of forces

Each of four beams has the same length and is acted on by three forces. Which beam has both no resultant force and no resultant torque acting on it?

Equilibrium of forces

The diagrams illustrate the forces acting on different bodies. Which body is unable to be in equilibrium?

Equilibrium of forces

A car moving at a speed of $28\,\text{m s}^{-1}$ leaves a motorway via an exit road. The far end of the exit road is $22\,\text{m}$ above the motorway. If gravity is the only force taken into account, what speed will the car have at the end of the exit road?

Gravitational potential energy and kinetic energy

A piston in a gas supply pump has a cross-sectional area of $400\,\text{cm}^2$ and travels a distance of $25\,\text{cm}$ in one stroke. The pump pushes the gas against a constant pressure of $3000\,\text{Pa}$. Calculate the work done by the piston in one stroke.

Density and pressure

Two physical quantities $P$ and $Q$ are combined. Their total is $R$, as shown. Which quantity could $P$ and $Q$ represent?

Scalars and vectors

The input and output for a transformer are given below. Input: potential difference $11000\,\text{V}$, current $28\,\text{A}$. Output: potential difference $240\,\text{V}$, current $1200\,\text{A}$. Determine the efficiency of the transformer.

Potential difference and power

The diagram illustrates a hydroelectric power station. The reservoir is connected to the turbines by a pipe with a uniform cross-sectional area. Water moves from the reservoir, along the pipe and through the turbines at a steady rate. Which statement about how the energy of the water changes as it travels from X to Y is correct?

Gravitational potential energy and kinetic energy

Which row gives the correct arrangement and movement of the molecules in water and in ice when both are at a temperature of $0^{\circ}\text{C}$?

Atoms, nuclei and radiation

The diagram represents a rectangular block with mass $8.2\,\text{kg}$ submerged in sea water whose density is $1.10 \times 10^{3}\,\text{kg m}^{-3}$. What is the pressure difference between the block’s upper and lower surfaces?

Density and pressure

A trolley is kept stationary between two steel springs. Each spring begins with an unstretched length of $0.10\,\text{m}$. Spring P has spring constant $60\,\text{N m}^{-1}$. Spring Q has spring constant $120\,\text{N m}^{-1}$. The extension of spring P is $0.40\,\text{m}$. What is the extension of spring Q?

Equilibrium of forces

A lift is held up by two steel cables, each with length $10\,\text{m}$ and diameter $0.5\,\text{cm}$. When a man with mass $80\,\text{kg}$ gets into the lift, it sinks by $1\,\text{mm}$. What is the best estimate of the value of the Young modulus of the steel?

Stress and strain

The diagram depicts a pipe containing air and open at both ends. The pipe has a length of $1.00\,\text{m}$, and a thin layer of fine sand coats the lower inner surface of the pipe. When a sound source of one frequency is placed close to one end of the pipe, resonance occurs in the air inside the pipe, and the sand pattern indicates that a standing wave with three nodes is produced in the pipe. The speed of sound in air is $330\,\text{m s}^{-1}$. What is the frequency of the sound?

Stationary waves

A stationary sound wave is produced in a measuring cylinder by blowing across the top, as shown. Which statement is correct?

Stationary waves

Diffraction is seen when a wave goes past an obstruction. It is most pronounced when the wavelength and the obstruction are about the same size. For waves moving through air, what pairing of wave and obstruction would show diffraction most clearly?

Diffraction

A safety inspector is determining the intensity of a sound. Close to a loudspeaker, his meter shows an intensity $I$. This is associated with an amplitude $A$ for the sound wave. At a different position, the meter shows an intensity reading of $2I$. What amplitude does the sound wave have there?

Progressive waves

A $1.5\,\text{V}$ cell delivers $0.20\,\text{A}$ to a lamp for seven hours until the lamp no longer works. What is a sensible estimate of the cell’s initial chemical energy content?

Energy conservation

The diagram illustrates two parallel plates. They are charged in such a way that an electric field exists between them. P, Q and R are points located at $\frac{1}{4}$, $\frac{1}{2}$ and $\frac{3}{4}$ of the separation from the top plate down to the bottom plate. What is the electric field strength at point P?

Potential difference and power

A charge of $2.6 \times 10^{-8}\,\text{C}$, which is positive, is in an electric field with a constant field strength of $300\,000\,\text{V m}^{-1}$. What amount of work is required to move the charge a distance of $4.0\,\text{mm}$ in the direction opposite to the field?

Potential difference and power

Which values of current and resistance would give a rate of energy transfer of $16\,\text{J s}^{-1}$?

Potential difference and power

A copper wire is pulled so that its diameter decreases from $1.0\,\text{mm}$ to a constant $0.5\,\text{mm}$. The resistance of the original copper wire is $0.2\,\Omega$. What is the resistance of the stretched wire?

Resistance and resistivity

Four statements concerning potential difference or electromotive force are given. 1. It is the conversion of electrical energy into other forms. 2. It is the conversion of other forms of energy into electrical energy. 3. It is the energy per unit charge needed to move charge all the way round a circuit. 4. It is the work done per unit charge as charge moves from one point to another. Which statements refer to potential difference, and which refer to electromotive force?

Potential difference and power

The diagram presents a four-terminal box linked to a battery and two ammeters. The readings on the two meters are the same. Which circuit inside the box will produce this outcome?

Kirchhoff's laws

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

Potential dividers

The diagram illustrates a resistor network. The potential difference across the network is $V$. Is the equation shown below valid for the network? $V = I\left(\frac{1}{R_1} + \frac{1}{R_2} + R_3\right)$

Kirchhoff's laws

A nuclear isotope gives out radiation that is picked up by a Geiger-Müller tube positioned about $10\ \text{cm}$ away from the radioactive source. The radiation is fully absorbed by a $2\ \text{mm}$ thick lead sheet. What can be deduced from this information about the emission from the isotope?

Atoms, nuclei and radiation

What stays unchanged during $\beta$-emission from a set of identical nuclei in a substance?

Atoms, nuclei and radiation

Three of these quantities share the same unit. Which quantity is measured in a different unit?

SI units

A graph plotted with neutron number on the vertical axis and proton number on the horizontal axis shows a chain of radioactive decays. Nucleus $X$ is the initial nucleus in the chain and, after the decays are complete, nucleus $Y$ is produced. What is emitted in the chain of decays?

Atoms, nuclei and radiation

A cathode-ray oscilloscope shows a square wave, as illustrated in the diagram. The time-base is set to $0.20\,\text{ms}$ per division. Find the frequency of the square wave.

Practical circuits

What can be done to reduce systematic errors when a measurement is taken?

Errors and uncertainties

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

Errors and uncertainties

A bicycle is braked so that it experiences uniform deceleration from a speed of $8\,\text{m s}^{-1}$ to $6\,\text{m s}^{-1}$ across a distance of $7\,\text{m}$. If the bicycle’s deceleration stays constant, what additional distance will it cover before it comes to rest?

Equations of motion

A ball is let go from rest above a horizontal surface. It rebounds once and then is caught. Which graph shows how the velocity $v$ of the ball changes with time $t$?

Equations of motion