May/June 2020

What would be a sensible estimate for the kinetic energy of a car moving at $30\,\text{m s}^{-1}$?

Gravitational potential energy and kinetic energy

A toy gun at rest fires a bullet. Immediately after it is fired, which statement about the bullet and the gun is not correct?

Linear momentum and its conservation

A wooden block is placed on the rough top surface of a board. The board is then lifted at one end until the block slides down it with constant velocity $v$. What describes the forces acting on the block while it is sliding at constant velocity?

Equilibrium of forces

Which statement gives the best description of a couple?

Turning effects of forces

A uniform rod XY, with weight $10.0\,\text{N}$, is freely hinged at X to a wall. As shown, it is kept level by 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

Four sets of vectors are illustrated, and each set shows every force acting on an object. All the forces lie in one plane. The object is in equilibrium. Which set of vectors could show the forces acting on the object?

Equilibrium of forces

A rectangular metal bar produces a pressure of $15\,200\,\text{Pa}$ on the level surface beneath it. The height of the metal bar is $80\,\text{cm}$. What is the density of the metal?

Density and pressure

A mass fixed to the bottom end of a spring moves up and down. At which positions along the mass’s motion are the gravitational potential energy of the mass (GPE), the elastic potential energy in the spring (EPE) and the kinetic energy of the mass (KE) at their maximum values?

Energy conservation

A block with weight $80\,\text{N}$ is moved a distance of $60\,\text{cm}$ along a slope that makes an angle of $30^\circ$ with the horizontal. The frictional force between the block and the slope surface is $25\,\text{N}$.\n\nWhat is the work $W_g$ done against the gravitational force and the work $W_f$ done against the frictional force?

Gravitational potential energy and kinetic energy

A ball is released from rest and falls towards the ground. Air resistance is negligible. Which graph shows how the height of the ball above the ground varies with speed?

Equations of motion

Power is passed through a machine, as shown. What is the machine’s efficiency?

Energy conservation

The vibration frequency $f$ of a mass $m$ held by a spring of spring constant $k$ is described by $f = C m^p k^q$ where $C$ is a constant with no units. State the values of $p$ and $q$?

Elastic and plastic behaviour

A tensile force is applied to stretch a sample of a material, then the force is taken away. The graph shows how the applied stress changes with strain. Which point on the graph could be the elastic limit for the material?

Elastic and plastic behaviour

A tensile force is applied to a rubber band that has not yet been stretched, so that it extends. The tensile force is then taken away. Which statement about the rubber band must be true?

Elastic and plastic behaviour

As it travels through air, a sound wave becomes less intense while its frequency remains constant. Which statement is the correct one?

Progressive waves

The graph shows how the displacement of an electromagnetic wave at one point varies with time. The wave is moving through a vacuum. What are the amplitude and the wavelength of the wave?

Progressive waves

A long glass tube is placed so that it is nearly fully submerged in a large tank of water. A tuning fork is sounded and held just above the tube’s open end while the tube is slowly lifted. A louder sound is heard for the first time when the height $h$ of the top of the tube above the water is $18.8\,\text{cm}$. The next louder sound is heard when $h$ is $56.4\,\text{cm}$. The speed of sound in air is $330\,\text{m s}^{-1}$. What is the frequency of the sound made by the tuning fork?

Stationary waves

A sound source producing a tone of one frequency $f_s$ moves at a steady speed straight toward an observer. It then goes past the observer and keeps moving straight away from the observer. The source velocity is unchanged. Which graph shows how the frequency $f_o$ of the sound detected by the observer varies with time?

Doppler effect for sound waves

What are the names of the electromagnetic waves whose wavelengths in a vacuum are $100\,\text{pm}$ and $100\,\mu\text{m}$?

Electromagnetic spectrum

The diagram depicts a string under tension between fixed endpoints $X$ and $Y$. A stationary wave is present on the string. The continuous curve represents the string at one extreme displacement. The dashed curve represents the string at the opposite extreme displacement. The central straight dashed line represents the equilibrium position of the string. Point $S$ on the string lies vertically above point $P$. Point $T$ on the string lies vertically below $Q$. Which statement is correct?

Stationary waves

Which condition has to be satisfied for diffraction to happen when a wave travels through a gap?

Diffraction

Monochromatic light of one wavelength is directed normally at two slits separated by $0.20\,\text{mm}$. Interference fringes are seen on a screen positioned $5.4\,\text{m}$ from the slits. The separation of adjacent bright fringes is $12\,\text{mm}$. What is the wavelength of the light?

Interference

The equation below gives the power generated when a force causes an object to move. $\text{power} = \frac{\text{work}}{\text{time}} = \frac{\text{force} \times \text{displacement}}{\text{time}}$ Which of these quantities are scalars, and which are vectors?

Scalars and vectors

A diffraction grating and a screen are used to find the single wavelength $\lambda$ of the light emitted by a source. Which feature is essential in this experiment?

The diffraction grating

A small charge $q$ is located in the electric field produced by a large charge $Q$. Each of the two charges is acted on by a force $F$. What is the electric field strength due to charge $Q$ at the location of charge $q$?

Physical quantities

A charged particle is located in a vacuum between two horizontal metal plates, as illustrated. The particle’s acceleration is $7.15 \times 10^{11}\,\text{m s}^{-2}$ downward. Its mass is $3.34 \times 10^{-27}\,\text{kg}$. Calculate the charge on the particle.

Potential difference and power

In the circuit diagram shown, the current is $3.2\,\text{mA}$. What is the direction of electron flow through resistor $R$, and what is the rate at which electrons flow through it?

Electric current

Which graph most accurately shows how the current $I$ through a filament lamp changes with the potential difference $V$ across the lamp?

Resistance and resistivity

A cylindrical metal wire $X$ has resistance $R$. The same volume of this metal is reshaped into a cylindrical wire $Y$ with twice the length. What resistance does wire $Y$ have?

Resistance and resistivity

A cell with electromotive force (e.m.f.) $E$ and internal resistance $r$ is connected across a resistor of resistance $R$. The resistor is able to dissipate a maximum power $P$ without overheating. What is the greatest value of $E$ for which the resistor does not overheat?

Potential difference and power

It is possible to join three identical resistors in four distinct arrangements. Two of these arrangements have resistances of $4.0\,\Omega$ and $9.0\,\Omega$. Determine the resistance of one resistor.

Resistance and resistivity

In the circuit diagram, a battery with negligible internal resistance is joined in series with two fixed resistors $R_1$ and $R_2$. The arrangement is intended to check whether the electromotive force (e.m.f.) of a certain cell is $1.5\,\text{V}$. The cell is placed between terminals $X$ and $Y$, in parallel with $R_2$ and in series with a galvanometer. Which statement about this check is correct?

Potential dividers

An element exists in two isotopic forms. What are the nuclear structures of these two isotopes?

Atoms, nuclei and radiation

A cathode-ray oscilloscope shows a square wave, as illustrated. The time-base setting is $0.20\,\text{ms}$ per division. What is the frequency of the square wave?

Practical circuits

A hadron carries charge $+e$, with $e$ being the elementary charge. Which arrangement of up ($u$) and down ($d$) quarks might make up this hadron?

Fundamental particles

A reading is made properly, but using a ruler that is at a much higher temperature than the one at which it was calibrated. Because of this increased temperature, the ruler expands. What effect does the higher temperature have on the reading, and how can the reading be made more accurate?

Errors and uncertainties

The electric car's velocity varies as shown. What acceleration does the car have?

Equations of motion

A projectile is launched from point $P$ with velocity $V$ at an angle $\theta$ to the horizontal. It reaches point $Q$, which is a horizontal distance $R$ from $P$, after a time $T$. The acceleration of free fall is $g$. Air resistance is negligible. Which equation is correct?

Equations of motion

A car starts from rest and moves in a straight line with constant acceleration. Which graph shows how the momentum $p$ of the car changes with the distance $s$ it travels?

Equations of motion

For a raindrop of mass $m$ descending with speed $v$, the resultant force $F$ is described by the equation $F = mg - kv^2$, where $k$ is a constant and $g$ is the acceleration of free fall. What is the raindrop’s velocity when it has reached a constant (terminal) velocity?

Momentum and Newton's laws of motion

What would be a sensible estimate for the mass of a raindrop?

Density and pressure

The diagrams illustrate a negative electric charge placed in a uniform electric field and a mass placed in a uniform gravitational field. Which row indicates the directions of the forces acting on the charge and on the mass?

Scalars and vectors

A bicycle pedal is linked to a pivot by a metal bar, as illustrated. The force acting on the pedal is $60\,\text{N}$ vertically downward. What is the moment of this force about the pivot?

Turning effects of forces

A slender horizontal beam XY is attached by a free hinge at point Y to a vertical wall. The beam is kept in equilibrium by a cable XZ fixed to the wall at point Z. A weight $W$ acts on the beam at point X. The force in the cable is $F_C$, and the force in the beam is $F_B$ respectively. Which vector triangle shows the forces on point X?

Equilibrium of forces

A pipe with one end open is floating in a liquid, as illustrated. The pipe has a cross-sectional area of $0.012\,\text{m}^2$. Its weight is $32\,\text{N}$. What is the density of the liquid?

Density and pressure

Over a period of time, fuel provides a car with energy $X$. Part of this energy becomes kinetic energy while the car speeds up. The remaining energy $Y$ is transferred away as thermal energy. What is the efficiency of the car?

Energy conservation

Under which situation is work done on an object?

Energy conservation

One end of a spring is fastened to a fixed point. A mass is then suspended from the spring’s other end. When the system is in equilibrium, the spring has an extension $x$. The graph shows how the tension in the spring varies with its extension. Which of the following statements is correct?

Elastic and plastic behaviour

An escalator in an underground station is carrying $25$ people and is travelling at a speed of $4.3\,\text{m s}^{-1}$. The mean mass of a person is $78\,\text{kg}$, and the escalator is at an angle of $40^\circ$ to the horizontal. What is the minimum power needed to lift these people?

Gravitational potential energy and kinetic energy

An elastic cord has an unstretched total length of $16.0\,\text{cm}$ and a cross-sectional area of $2.0 \times 10^{-6}\,\text{m}^2$. It is kept horizontal by two smooth pins that are $8.0\,\text{cm}$ apart. The cord follows Hooke’s law. A load with mass $0.40\,\text{kg}$ is hung at the centre of the cord. The angle between the two sections of cord supporting the load is $60^\circ$. Determine the Young modulus of the cord material.

Stress and strain

A student is examining the mechanical properties of a metal. He loads a long, thin wire with a range of weights up to the point at which it breaks, and records the extension of the wire for every load. He then draws a graph of stress against strain. The student repeats the experiment using a wire made of the same metal, but with twice the initial length and half the diameter. Which graph is obtained?

Stress and strain

Which of the quantities is a scalar?

Scalars and vectors

Which statement explains the meaning of plastic deformation of a material?

Elastic and plastic behaviour

A transverse wave travels along a rope. Two points X and Y on the rope are separated by a quarter of a wavelength. Which statement about the two points X and Y cannot be true at any moment?

Progressive waves

Two progressive waves are incident at a stationary point P. The graph shows how the displacement of each wave at point P changes with time. What is the phase difference between the two waves at point P?

Progressive waves

A microphone that is linked to the Y-plates of a cathode-ray oscilloscope (CRO) is positioned in front of a loudspeaker. The CRO screen shows the trace. The time-base setting is $0.5\,\text{s cm}^{-1}$ and the Y-plate sensitivity is $0.2\,\text{mV cm}^{-1}$. Determine the frequency of the sound produced by the loudspeaker and the amplitude of the CRO trace.

Progressive waves

The diagram illustrates an experiment used to form a stationary wave in an air column. A tuning fork positioned above the column vibrates and generates a sound wave. The length of the air column may be changed by adjusting the amount of water in the tube. The tube is filled and then the water is allowed to drain out. The first two stationary waves are produced when the air column lengths are $0.14\,\text{m}$ and $0.42\,\text{m}$. What is the wavelength of the sound wave?

Stationary waves

A person who is not moving measures the speed and wavelength of the sound produced by a horn on a vehicle that is also not moving. The person then carries out the measurements again while the vehicle is moving towards them at a constant speed. Which row states the measured wavelength and the measured speed of the sound wave from the moving vehicle in comparison with the sound wave from the vehicle at rest?

Doppler effect for sound waves

The table presents the wavelengths of five electromagnetic waves. Which row correctly names the principal radiation for each of these wavelengths?

Electromagnetic spectrum

Two progressive waves overlap at one point. What condition has to be satisfied for superposition of the waves to take place?

Progressive waves

A hill lies between a television (TV) transmitter and a house. The transmitter is not visible from the house, but TV reception there is good. Which wave effect at the hill allows the TV signal to reach the house?

Diffraction

The diagram illustrates an arrangement set up to show two-source interference with coherent light of a single wavelength $\lambda$. An interference pattern is seen on a screen $3.0\,\text{m}$ from slits X and Y, and the slit separation is $1.0\,\text{mm}$. The central bright fringe is located at Q, and P is the second bright fringe from the centre. What is the separation between Q and P?

Interference

A galvanometer with resistance $5\,\Omega$ is intended for use in a null method. To prevent the galvanometer from being damaged by an excessively large initial current, resistors with resistance $0.5\,\Omega$ and $1\,\text{k}\Omega$ are available. Which arrangement would give this protection?

Practical circuits

Light of wavelength $\lambda$ is incident at normal incidence on a diffraction grating. The angle between the second-order maximum and the normal to the grating is $\theta$. The graph shows how $\lambda$ varies with $\sin\theta$. How many lines per millimetre are there on the diffraction grating?

The diffraction grating

A dipole consists of two charges with equal magnitude: one positive and one negative. The electric field pattern for a dipole is shown below. At point X, in what direction does the force act on an electron?

Scalars and vectors

A charged oil droplet with mass $m$ falls, at first freely, in a vacuum between two horizontal metal plates separated by a distance $x$. A potential difference (p.d.) $V$ is then applied across the plates. As a result, the oil droplet keeps accelerating downwards, but now with a smaller acceleration $a$. The polarity of the applied p.d. is then reversed so that the direction of the electric force on the droplet is also reversed. This causes the downward acceleration of the oil droplet to increase to $3a$. Determine the magnitude of the charge on the oil droplet.

Potential difference and power

The number density of free electrons in copper is $8.0 \times 10^{28}\,\text{m}^{-3}$. A copper wire has diameter $0.42\,\text{mm}$. Determine the average drift speed of the free electrons in the wire when the current in the wire is $0.57\,\text{A}$?

Electric current

An electric kettle has a power rating of $2.0\,\text{kW}$, which gives the rate at which energy is delivered to the heating coil inside the kettle. The coil's resistance is $5.0\,\text{k}\Omega$. What current flows in the coil?

Potential difference and power

A conductor is made from three wires joined in series. All three wires are made from the same metal, although each has a different cross-sectional area. A current $I$ flows in the conductor. Point Y on the conductor has zero potential. Which graph best represents how the potential $V$ changes with distance along the conductor?

Potential dividers

A cell with electromotive force (e.m.f.) $E$ and internal resistance of $0.50\,\Omega$ is connected to a resistor whose resistance is $4.7\,\Omega$. The greatest power the resistor can dissipate without becoming overheated is $0.50\,\text{W}$. What is the largest value of $E$ so that the resistor does not overheat?

Potential difference and power

Kirchhoff’s first and second laws are associated with the conservation of physical quantities. Which quantities do they relate to?

Kirchhoff's laws

In the circuit diagram, X is a variable resistor and its resistance may be altered from $5.0\,\Omega$ to $500\,\Omega$. The electromotive force (e.m.f.) of the battery is $12.0\,\text{V}$. Its internal resistance is negligible. What is the greatest possible range of values of potential difference across the output?

Potential dividers

An unstable nucleus passes through a chain of decays and becomes a stable nucleus at the end. The starting nucleus and the final nucleus are isotopes of one another. How many $\alpha$ and $\beta^-$ particles might have been released during the decay chain?

Atoms, nuclei and radiation

Measurements are taken of the current $I$ at different voltages $V$ across a fixed resistor. The outcomes are then plotted on a graph to show how $I$ varies with $V$. What is the most appropriate description of the errors in the readings?

Resistance and resistivity

A hadron has charge $-e$ and is made up of three quarks. What might the quark composition of this hadron be?

Fundamental particles

A stone is released from a point $20\,\text{m}$ above the water surface. The graph shows how the stone’s velocity changes with time. Which statement gives the stone’s approximate position four seconds after it is released?

Equations of motion

Car X moves at a constant speed $u$ along a straight section of road. When $t = 0$, a second car Y is $d_0$ behind car X and is moving in the same direction at speed $v$. The speed $v$ is smaller than the speed $u$. At $t = 0$, car Y starts to accelerate at a constant rate. Car Y passes car X at $t = T$. Which graph would most suitably represent how the distance $d$ between the cars changes with time $t$?

Equations of motion

The resultant force acting on an object is gradually increased. Which graph could represent how the momentum $p$ of the object changes with time $t$?

Momentum and Newton's laws of motion

An astronaut weighs $660\,\text{N}$ while standing on the Earth’s surface. The acceleration of free fall on the surface of Mars is $3.71\,\text{m s}^{-2}$. What would the astronaut’s weight be if she were standing on the surface of Mars?

Momentum and Newton's laws of motion

A mass $m_1$ moving at speed $u_1$ collides with a mass $m_2$ moving at speed $u_2$ in the same direction. Following the collision, mass $m_1$ has speed $v_1$ and mass $m_2$ has speed $v_2$ in the same direction. The collision is perfectly elastic. Which equation is not correct?

Linear momentum and its conservation

A man is taking part in a race along a straight path. What is an approximate value of his kinetic energy?

Gravitational potential energy and kinetic energy

A ball of mass $m$, travelling with velocity $v$, strikes a second ball of mass $2m$ that is stationary. The two balls remain joined together. What fraction of the original kinetic energy is lost during the collision?

Linear momentum and its conservation

A submarine is in equilibrium while it is completely underwater. What produces the upthrust acting on the submarine?

Density and pressure

Two forces, each having magnitude $F$, are applied along the sides of a rectangular metal plate, as illustrated. The plate measures length $a$ and width $b$. What is the torque about point $P$?

Turning effects of forces

A rod that is not uniform has a mass of $100\,\text{g}$ and a length of $50\,\text{cm}$. A chain supports it at its midpoint. Equilibrium is maintained by suspending a mass of $60\,\text{g}$ from the right-hand end, as shown. The centre of gravity of the rod is at a distance $d$ from its left-hand end. What is the value of $d$?

Turning effects of forces

A light rigid rod $XY$ carries an object of weight $W$ attached at one end. The rod is balanced in equilibrium, supported at $Z$ and against a vertical wall at $X$. As shown, the support applies a force $R$ to the rod. The diagram indicates the directions, but not the sizes, of the forces $R$ and $W$. What is the direction of the force acting on the rod at $X$?

Equilibrium of forces

Liquid $Q$ has a density that is twice that of liquid $R$. In liquid $R$, the pressure from the liquid at depth $x$ is $4\,\text{kPa}$. At what depth in liquid $Q$ will the pressure from the liquid be $7\,\text{kPa}$?

Density and pressure

A trolley is initially at rest at X. It moves down to Y and finally stops at Z. Which row could summarise the energy changes during this process?

Gravitational potential energy and kinetic energy

A cylinder is heated, so the air trapped inside expands while the pressure remains constant at $2.2 \times 10^5\,\text{Pa}$. As the air expands, the piston moves upward by $0.50\,\text{m}$ and does $11\,\text{kJ}$ of work. Frictional effects are negligible. What is the area of the piston’s cross-section?

Density and pressure

A ball moves down a curved track, as illustrated. Point X is $0.40\,\text{m}$ higher than point Y. At point X, the ball’s speed is $2.5\,\text{m s}^{-1}$. Frictional forces may be ignored. What is the speed of the ball at point Y?

Energy conservation

The force diagram represents an aircraft that is speeding up. At the moment shown, the aircraft’s velocity is $40\,\text{m s}^{-1}$. At what rate is its kinetic energy increasing?

Energy conservation

A gas sample has a mass of $4.8\,\mu\text{g}$ and takes up a volume of $1.2\,\text{dm}^3$. What is the density of the gas sample?

Density and pressure

The diagram depicts a simplified building model containing four identical heavy floors. The gap from the ground to the bottom floor is twice the separation between neighbouring floors. Between successive floors are equal numbers of vertical steel support rods whose mass is negligible compared with that of the floors. The rods have different diameters so that the stress in every rod is the same. What is the ratio $\dfrac{\text{diameter of bottom rods}}{\text{diameter of top rods}}$?

Stress and strain

When a rabbit jumps, the Achilles tendon in its leg is extended. The graph shows how the tendon’s length changes with tension. Calculate the strain energy in the tendon when the tension is $400\,\text{N}$?

Elastic and plastic behaviour

A wave with amplitude $A$ has intensity $I$. When it travels through a particular medium, its intensity becomes $\dfrac{I}{4}$. What is the wave’s new amplitude?

Progressive waves

A wave moves along a coiled spring. The graph shows how the displacement of a point on the spring changes with time. What is the frequency of the wave?

Progressive waves

A loudspeaker is positioned at the open end of a tube that is closed and contains powder. When the loudspeaker emits sound at frequency $1200\,\text{Hz}$, a stationary wave forms in the tube. The powder collects at the nodes of the stationary wave, as shown. The speed of sound in air is $336\,\text{m s}^{-1}$. What is the value of distance $x$?

Stationary waves

A sound wave with frequency $f$ is produced by a source S that is not moving. The source then travels away from an observer who remains stationary. Which statement is correct?

Doppler effect for sound waves

The table shows the possible wavelengths for four different electromagnetic waves. Which row is correct?

Electromagnetic spectrum

A vertical tube is partly filled with water. A sound wave travels down the tube and is reflected from the water surface. The frequency of the sound wave is increased gradually from zero until a much louder sound is heard. Water is then taken out of the tube until a second much louder sound is heard. Which diagram shows the new pattern of the stationary wave that is formed?

Stationary waves

Water waves in a ripple tank are arranged to travel through a narrow gap, as shown. Which diagram indicates the waves after they have gone through the gap?

Diffraction

A double-slit interference experiment is arranged with green light. Interference fringes are produced on a screen. Which one change would make the fringes farther apart?

Interference

What features does a vector quantity have that a scalar quantity does not have?

Scalars and vectors

Monochromatic light from a distant point source is incident normally on a diffraction grating whose lines are arranged vertically. The plane of the diffraction grating is perpendicular to the incident light. A student observes the grating from a position close to it. What could the student see?

The diffraction grating

Which diagram most accurately shows the electric field between two point charges with equal magnitude but opposite sign?

Potential difference and power

An oil drop carrying negative charge and having mass $m$ is located between two horizontal metal plates that are parallel and separated by a distance $d$. With a potential difference (p.d.) of $V_1$ across the plates, the drop moves upwards with constant speed. If the p.d. is reduced to $V_2$, the drop moves downwards with the same constant speed. Whenever the drop is in motion, air resistance acts on it. The upthrust on the drop is negligible. The acceleration of free fall is $g$. What is the charge on the oil drop?

Equilibrium of forces

The unit used for electric charge is the coulomb. What does 1 coulomb represent?

Electric current

As illustrated, two copper wires are connected together and a current flows through them. Wire P has diameter $d$, whereas wire Q has diameter $2d$. What is the ratio $\frac{\text{average drift speed of the free electrons in wire P}}{\text{average drift speed of the free electrons in wire Q}}$ ?

Electric current

The circuit shown is supplied by a source with electromotive force (e.m.f.) $V$ and negligible internal resistance. A current of $3.0\,\text{A}$ flows through the $4.0\,\Omega$ resistor. What value does $V$ have?

Kirchhoff's laws

A heating-element wire has resistance $R$. It snaps and a different wire is fitted in its place. The table gives data for the original wire and the replacement wire. Original wire: length $l$, diameter $d$, resistivity of metal $\rho$. Replacement wire: length $l$, diameter $2d$, resistivity of metal $2\rho$. What is the resistance of the replacement wire?

Resistance and resistivity

A fixed resistor and a variable resistor are joined in series to a cell with internal resistance, as illustrated. The graph plots how a quantity $X$ changes with the resistance $R$ of the variable resistor as $R$ is raised from zero to its greatest value. What might $X$ stand for?

Potential difference and power

An e.m.f. cell of $4.0\,\text{V}$, with negligible internal resistance, is linked to a fixed resistor of resistance $1.0\,\Omega$ and a potentiometer with maximum resistance $3.0\,\Omega$, as shown. What range of potential differences is available between terminals X and Y?

Potential dividers

Radiation produced by a radioactive source travels only a few millimetres in air and is deflected by an electric field. What type of radiation is being emitted?

Atoms, nuclei and radiation

An electric circuit has been arranged to find the resistance of a $12\ \text{V}$, $1.2\ \text{W}$ lamp while it is working normally. An analogue ammeter and an analogue voltmeter are employed. Which meter ranges would be the most appropriate?

Practical circuits

Which equation represents the process of $\beta^+$ decay? Key: $u$ stands for the up quark $d$ denotes the down quark $\nu$ = (electron) neutrino $\bar{\nu}$ = (electron) antineutrino

Fundamental particles

Two liquid-in-glass thermometers in a liquid that is well mixed are each separately read by $10$ different students. Every student records that one thermometer shows $21\,^{\circ}\text{C}$ and the other shows $23\,^{\circ}\text{C}$. What might account for the discrepancy?

Errors and uncertainties

The graph illustrates how the velocity of a ball changes with time from the instant it is struck vertically upwards from the ground. What is the displacement of the ball from the ground after a time of $3.0\,\text{s}$?

Equations of motion

Two students each launch a ball horizontally from the top of a tower, and both balls are released at the same instant. The first student sends her ball at a speed of $20\,\text{m s}^{-1}$, while the second student sends his ball at a speed of $10\,\text{m s}^{-1}$. Take air resistance as negligible and assume that the balls strike level ground. Which row gives the horizontal distances covered and the times taken to land for the two balls on the ground?

Equations of motion

A ball of mass $m$ moves vertically downward and then strikes a horizontal floor with speed $u$. It bounces vertically upward with speed $v$. The impact lasts for a time $\Delta t$. What is the average resultant force exerted on the ball during the collision?

Momentum and Newton's laws of motion

For a raindrop of mass $m$ descending vertically at speed $v$, the resultant force $F$ is described by $F = mg - kv^2$ in which $k$ is a constant and $g$ represents the acceleration of free fall. As the raindrop falls, it finally attains a constant (terminal) velocity. Which graph shows how the terminal velocity of the raindrop varies with mass $m$?

Momentum and Newton's laws of motion