May/June 2022

Which term refers to a physical quantity?

Physical quantities

What does the principle of conservation of momentum state?

Linear momentum and its conservation

A wooden plank is arranged horizontally and pivots at one end, as illustrated. Its mass is $100\,\text{kg}$ and its length is $10\,\text{m}$. The plank’s centre of gravity lies $4\,\text{m}$ from the pivot. What is the moment of the plank’s weight about the pivot?

Turning effects of forces

At what time is an object in equilibrium?

Equilibrium of forces

A diving board of uniform density is supported by two fixed rods at points $P$ and $Q$. A person stands at the end $R$ of the diving board, as shown. The forces from the rods acting on the board are vertical. The board stays in equilibrium while the person moves slowly from $R$ towards point $Q$. Which row shows how the magnitudes of the forces from the rods on the board change?

Equilibrium of forces

A solid block has dimensions $L$, $2L$ and $4L$. It is placed in water of uniform density with the faces of greatest area lying horizontally, as illustrated. The upthrust on the block is $U$. The block is then turned into a different orientation so that the faces of least area are horizontal. The block stays completely submerged in the water. What is the upthrust acting on the block in its new orientation?

Density and pressure

Inside a sizeable vessel at an oil refinery, three oils with different densities are blended together. No chemical reaction takes place. The mixture contains: 1200 kg of oil with density $1100\ \text{kg m}^{-3}$ 1500 kg of oil with density $860\ \text{kg m}^{-3}$ 4000 kg of oil with density $910\ \text{kg m}^{-3}$. What is the density of the mixture?

Density and pressure

A box travels down a rough ramp. The box’s gravitational potential energy changes by $16\ \text{J}$ as it moves from position X to position Y. At X, the box has kinetic energy of $24\ \text{J}$, and at Y it has kinetic energy of $35\ \text{J}$. How much work is done against the frictional force?

Energy conservation

An electric motor is given a total energy of $E$. A quantity of energy, $Q$, is wasted, while the rest is used for useful work. What is the efficiency of the motor?

Energy conservation

Several objects of unequal mass are positioned on the flat surface of a table. They are then lifted to different heights above the table. Each object has the same increase in gravitational potential energy. Which graph most accurately represents how the height $h$ of the objects above the table changes with their mass $m$?

Gravitational potential energy and kinetic energy

Wires P and Q are each made from the same metal and are suspended vertically from a steel support beam. Wire Q is half the length of wire P and has twice the diameter of wire P. The same masses are hung from the lower end of each wire. As the masses stretch the wires, both wires obey Hooke’s law. What is the value of $\frac{\text{extension of wire P}}{\text{extension of wire Q}}$?

Stress and strain

Which two units are the same when written in terms of SI base units?

SI units

Which of the following statements about elastic and plastic deformation has to be correct?

Elastic and plastic behaviour

The graph illustrates how the displacement of a particle changes with time as a progressive wave moves through it. What are the wave’s frequency and amplitude?

Progressive waves

The graph indicates how the displacement of an air particle changes with time as a sound wave moves through air. The sound intensity is reduced to half, while the frequency stays the same. The four graphs below are drawn on the same scale as the graph above. Which graph represents the displacement of the air particle?

Progressive waves

Which of the following statements is correct?

Physical quantities

A car is moving with a constant velocity straight towards a man who is standing in the centre of the road. The driver uses the car’s horn to give a warning. The horn produces a sound wave with a constant frequency. The frequency of the sound received by the man is not the same as the frequency of the sound produced by the horn. Which statement is correct?

Doppler effect for sound waves

Which of the following statements about electromagnetic waves is correct?

Electromagnetic spectrum

A stationary wave forms on a string stretched between two fixed points separated by $48\,\text{cm}$. At one particular instant, the string looks as shown. What is the wavelength of the stationary wave?

Stationary waves

A pipe is sealed at one end and has a loudspeaker at the open end. For certain sound frequencies from the loudspeaker, a stationary sound wave is produced in the air inside the pipe, with an antinode at the open end of the pipe. The pipe length is $0.85\,\text{m}$. The speed of sound in air is $340\,\text{m s}^{-1}$. Which frequency of sound from the loudspeaker would not create a stationary wave?

Stationary waves

Water waves with wavelength $\lambda$ are travelling normally towards an obstacle that has a narrow opening. The opening has a width equal to $\lambda$. The waves leaving the opening spread out through an angle $\theta$, as illustrated. The opening is then gradually made wider. What, if anything, happens to $\theta$ and to the wavelength of the waves after they pass through?

Diffraction

Monochromatic light passes through two narrow slits and forms an interference pattern on a screen positioned some distance away. The interference fringes are very close together. Which change would make the separation between the fringes larger?

Interference

The acceleration of free fall on Earth is stated as $(10 \pm 2)\,\text{m s}^{-2}$. Which statement is correct?

Errors and uncertainties

Light with wavelength $5.4 \times 10^{-7}\,\text{m}$ is directed normally onto a diffraction grating. The spacing between neighbouring lines in the grating is $2.0 \times 10^{-6}\,\text{m}$. The light leaving the grating is received by a semicircular screen, as shown in the view from above. The grating is positioned at the centre of the semicircle, and the grating lines are vertical. How many bright spots are produced on the screen?

The diffraction grating

A copper wire that is straight and has a diameter of $0.42 \times 10^{-3}\,\text{m}$ contains free electrons with a number density of $8.5 \times 10^{28}\,\text{m}^{-3}$. During one time interval, a charge of $0.15\,\text{C}$ passes along the wire. What is the mean displacement of the free electrons along the wire over this time interval?

Electric current

What is meant by the potential difference (p.d.) across a component?

Potential difference and power

The graph illustrates the $I$-$V$ characteristic of a semiconductor diode. Which statement can be deduced from the graph?

Practical circuits

A wire has a resistance of $30\,\Omega$. A second wire is made from the same material, has the same mass and is three times the length of the first wire. What is the resistance of the second wire?

Resistance and resistivity

A cell has internal resistance $r$ and electromotive force (e.m.f.) $E$. The cell is placed in series with an ammeter and a variable resistor with resistance $R$. When $R$ is $10\,\Omega$ the ammeter shows $0.3\,\text{A}$. When $R$ is $5\,\Omega$ the ammeter shows $0.4\,\text{A}$. What is the value of $E$?

Practical circuits

In an electrical circuit, the total current flowing into a junction is always the same as the total current flowing out of it. Why does this happen?

Kirchhoff's laws

For the circuits illustrated, the temperature is held constant. In which circuit does the potential difference (p.d.) $V$ increase as light intensity rises?

Potential dividers

Carbon-14 undergoes decay to nitrogen-14 by releasing a $\beta^-$ particle. Which statement describes why the emitted $\beta^-$ particles have a spread of different kinetic energies?

Atoms, nuclei and radiation

A nucleus of a radioactive element emits an $\alpha$-particle, then a $\beta^-$ particle, and afterwards another $\beta^-$ particle. Which statement gives the description of the final element produced?

Atoms, nuclei and radiation

Two cables are fixed to a bracket and apply forces as illustrated. What are the magnitudes of the resultant’s horizontal and vertical components from the two forces?

Scalars and vectors

In the nucleus of ${}^{9}_{4}\text{Be}$, how many hadrons, baryons and mesons are present?

Atoms, nuclei and radiation

The curved line PQR represents the velocity-time graph of a car that begins from rest. Find the car’s average acceleration during the first $5\,\text{s}$?

Equations of motion

A ball is launched horizontally at a speed of $10.0\,\text{m s}^{-1}$ over level ground. It reaches the ground after $3.0\,\text{s}$. Air resistance is negligible. What is the speed of the ball immediately before impact?

Equations of motion

An object travels in a straight line across the ground at a constant speed. Which statement about the resultant force acting on the object is correct?

Momentum and Newton's laws of motion

Water emerges from a pipe and strikes a wall. As the water jet reaches the wall, its horizontal speed is $v$ and its cross-sectional area is $A$. The density of the water is $\rho$. The water does not rebound from the wall. What force does the water exert on the wall?

Momentum and Newton's laws of motion

A projectile is fired at an angle to horizontal ground and moves through the air. It is at its greatest height at position $X$. Assume that no upthrust acts on the projectile. Which diagram shows the direction or directions of the force or forces acting on the projectile at position $X$?

Momentum and Newton's laws of motion

Which estimate would be sensible?

Physical quantities

Ball X and ball Y travel towards one another at speeds of $5\,\text{m s}^{-1}$ and $15\,\text{m s}^{-1}$ respectively. They undergo a perfectly elastic head-on collision, and ball Y then moves to the right at a speed of $7\,\text{m s}^{-1}$. What is the speed and direction of ball X following the collision?

Linear momentum and its conservation

A couple is produced by two forces. Which statement describes these two forces?

Turning effects of forces

A uniform rod is hinged to a wall at one end. Its other end is held up by a wire, keeping the rod horizontal and in equilibrium. Which arrow indicates the direction of the force exerted on the rod by the hinge?

Equilibrium of forces

A diving board has length $5.0\,\text{m}$ and is hinged at one end. It is held up $2.0\,\text{m}$ from that end by a spring with spring constant $10\,\text{kN m}^{-1}$. A child with mass $40\,\text{kg}$ stands at the outer end of the board. What additional compression does the spring experience because of the child standing on the end of the board?

Turning effects of forces

A granite rock located at the Earth's surface has density $\rho$. It is then moved to the surface of a different planet. The acceleration of free fall at the surface of the other planet is 2 times the value at the Earth's surface. What is the density of the rock on the other planet?

Density and pressure

A sealed U-shaped tube holds a liquid of density $\rho$ that is at rest. On one side of the tube there is a gas at pressure $p_1$, and on the other side there is a gas at pressure $p_2$, as illustrated. The acceleration of free fall is $g$. Which equation is correct?

Density and pressure

Power is equal to the product of which two quantities?

Potential difference and power

A new kind of filament lamp has been created by researchers and it has an efficiency of $40\%$. The efficiency of older filament lamps is $5.0\%$. Both lamp types give the same useful output power. What is the ratio $\dfrac{\text{input power to new type of lamp}}{\text{input power to old type of lamp}}$?

Energy conservation

A student tries to derive the expression for kinetic energy $E_K$. She starts with an object of mass $m$ that is initially stationary. A constant force $F$ acting on the object makes it accelerate to a final velocity $v$ over a displacement $s$. The kinetic energy gained by the object is equal to the work done on the object by the force $F$. Which equation would the student not need in order to derive the formula for $E_K$?

Gravitational potential energy and kinetic energy

A metal wire follows Hooke’s law and has a Young modulus of $2.0 \times 10^{11}\,\text{Pa}$. Its initial length is $1.6\,\text{m}$ and its diameter is $0.48 \times 10^{-3}\,\text{m}$. Determine the spring constant of the wire.

Stress and strain

What symbol represents the SI base unit of temperature?

SI units

A wire is under a tensile force that is stretching it. Which statement about the elastic limit has to be true?

Elastic and plastic behaviour

Which statement is true for every type of progressive wave?

Progressive waves

A transverse water wave is travelling across the surface of water. As the ball floats on the surface, it moves up and down, but not sideways. At one moment, the ball is at the position illustrated. The wave has a frequency of $0.20\,\text{Hz}$ and an amplitude of $0.70\,\text{m}$. The separation between a trough and a neighbouring peak is $2.4\,\text{m}$. How far does the ball travel in $20\,\text{s}$?

Transverse and longitudinal waves

A sound wave moves from left to right through a room. The change, with distance across the room, in the displacement of the air molecules at one instant is shown. At what distance is the air pressure at its lowest?

Progressive waves

A source produces a sound wave with one frequency. Owing to the Doppler effect, a stationary observer hears sound at a different frequency. What condition is necessary for the Doppler effect to happen?

Doppler effect for sound waves

An electromagnetic wave travelling in free space has a frequency of $2.5 \times 10^{14}\,\text{Hz}$. Which part of the electromagnetic spectrum contains this frequency?

Electromagnetic spectrum

Two polarising filters are positioned adjacent to one another with their planes aligned parallel. The transmission axis of the first polarising filter is inclined at $50^{\circ}$ to the vertical. The transmission axis of the second polarising filter is inclined at $20^{\circ}$ to the vertical. The separation angle between the transmission axes of the two polarising filters is $30^{\circ}$. A beam of vertically polarised light with intensity $8.0\,\text{W m}^{-2}$ falls normally on the first polarising filter. What is the intensity of the light emerging from the second polarising filter?

Polarisation

A stationary wave is established on a stretched string between points P and T. Which statement correctly describes the stationary wave?

Stationary waves

A bar oscillates at frequency $f$ to create water waves in a ripple tank. The waves then pass through an opening of width $x$ in a barrier, causing diffraction. Which pairing of vibration frequency and gap width will result in the smallest diffraction angle?

Diffraction

At an outdoor concert, there are two large speakers positioned next to the stage to project the music. To check the speakers, both are set to produce sound with the same wavelength and the same amplitude. The curved lines in the diagram show wavefronts. At which point is the sound loudest heard?

Interference

Which statement concerning systematic errors is incorrect?

Errors and uncertainties

The equation $\lambda = \dfrac{d \sin \theta}{n}$ is applied to determine the wavelength $\lambda$ of light in an experiment using a diffraction grating. The pattern produced by the diffraction grating is shown on a screen. What quantities do $n$ and $d$ stand for?

The diffraction grating

The diagram represents a metal block. Its sides have lengths $a$, $b$ and $c$, as indicated, and the block’s volume is $V$. Every charge carrier carries a charge of $-q$, and the number density of charge carriers in the metal is $n$. On average, each charge carrier needs time $t$ to travel through the block. What expression gives the current $I$?

Electric current

The circuit diagrams depict two lamps X and Y, each connected to a cell. For lamp X, the current is $0.50\,\text{A}$ and the resistance is $9.6\,\Omega$. For lamp Y, the current is $3.0\,\text{A}$ and the resistance is $1.2\,\Omega$. Find the ratio $\dfrac{\text{power in lamp X}}{\text{power in lamp Y}}$?

Potential difference and power

The light intensity falling on a light-dependent resistor (LDR) is increased. The temperature of a thermistor is increased. In each case, the current through the component is kept constant. What happens to the potential difference across each component?

Resistance and resistivity

An iron wire is $8.0\,\text{m}$ long and has a diameter of $0.50\,\text{mm}$. Its resistance is $R$. A second iron wire is $2.0\,\text{m}$ long and has a diameter of $1.0\,\text{mm}$. What resistance does the second wire have?

Resistance and resistivity

A cell that has a constant electromotive force (e.m.f.) is connected to a fixed resistor. With time, the cell’s internal resistance rises. What happens when the internal resistance rises?

Practical circuits

Kirchhoff’s first and second laws follow from the conservation of two different quantities. Which quantities are these?

Kirchhoff's laws

A potentiometer circuit is employed to find the electromotive force (e.m.f.) $E_X$ of a cell. The arrangement has a second cell with known e.m.f. $E_0$ and negligible internal resistance, together with a uniform resistance wire $PQ$ whose length is known. $E_X$ is smaller than $E_0$. The sliding contact $J$ may be placed at any point along the resistance wire. Which circuit is appropriate for finding $E_X$?

Practical circuits

In an experiment involving $\alpha$-particle scattering, $\alpha$-particles are aimed at a thin gold foil. The majority of the $\alpha$-particles pass directly through the foil, or are turned through only a small angle. A small number of $\alpha$-particles are turned through a large angle. Which statement cannot be deduced from this experiment?

Atoms, nuclei and radiation

The four nuclei are shown here. $^{{28}}_{{14}}\text{E}$, $^{{25}}_{{15}}\text{G}$, $^{{25}}_{{12}}\text{M}$, $^{{24}}_{{13}}\text{Q}$ Which of the following statements about these nuclei is correct?

Atoms, nuclei and radiation

An object is travelling with an initial velocity of $4.0\ \text{m s}^{-1}$ towards the right. Its velocity then changes to a final velocity of $3.0\ \text{m s}^{-1}$ downwards, as illustrated. Which arrow shows the change in velocity of the object?

Scalars and vectors

A neutron consists of one up ($u$) quark together with two down ($d$) quarks. If a neutron changes into a proton, a beta-particle is released. What change occurs in the neutron’s quark structure as a result of the emission of the beta-particle? (The symbol for a neutrino is $\nu_e$ and for an antineutrino is $\overline{\nu}_e$.)

Atoms, nuclei and radiation

A car moves anticlockwise around a horizontal circular road with radius $12\,\text{m}$, as illustrated. It takes $4.0\,\text{s}$ for the car to go from position P to position Q. What is the magnitude of the car’s average velocity for the trip from P to Q?

Non-uniform motion

In a deep well, the water surface is $78.0\,\text{m}$ below the top edge of the well. A person standing at the top lets a heavy stone fall down the well. Air resistance may be ignored. The speed of sound in air is $330\,\text{m s}^{-1}$. What is the time interval between the person releasing the stone and hearing it strike the water?

Equations of motion

Which statement is not one of the conditions for a pair of forces to obey Newton’s third law of motion?

Momentum and Newton's laws of motion

A child with mass $20\,\text{kg}$ is standing on the rough top surface of a sledge whose mass is $40\,\text{kg}$. The sledge is able to move along a horizontal surface with no friction. One end of a rope is fixed to the sledge. The rope goes round a stationary frictionless pole, and the child holds the free end of the rope, as illustrated. The rope remains horizontal. The child exerts a horizontal pull of $12\,\text{N}$ on the rope. As a result, the child and the sledge accelerate together with the same acceleration towards the pole. What is the frictional force acting between the child and the sledge?

Momentum and Newton's laws of motion

A stone S and a foam rubber ball R are two identical spheres with the same volume. They are let go from rest at time $t = 0$ and descend vertically through the air. Each one reaches terminal velocity. Which graph best represents how the speed $v$ of the stone and of the rubber ball changes with time $t$?

Non-uniform motion

Which pair of quantities count as physical quantities?

Physical quantities

A person is standing at the edge of a tall cliff beside the sea. The person throws a stone straight upwards. Air resistance acts on the stone. The stone later lands in the sea. Which velocity-time graph best represents the stone’s motion from the moment it is released until it reaches the sea?

Non-uniform motion

Skaters with masses $80\,\text{kg}$ and $40\,\text{kg}$ travel straight towards one another and then collide. Before the collision, the heavier skater is travelling to the right with a speed of $2.0\,\text{m s}^{-1}$, while the lighter skater is travelling to the left with a speed of $1.0\,\text{m s}^{-1}$. Following the collision, the heavier skater travels to the right with a speed of $0.80\,\text{m s}^{-1}$. What is the relative speed of separation of the two skaters?

Linear momentum and its conservation

Which statement describes the two forces that make up a couple?

Turning effects of forces

A wall-mounted street lamp is supported by a metal rod and a cable. Which vector triangle could show the forces acting on the end of the rod at point $P$?

Equilibrium of forces

An unknown mass and a $1.00\,\text{kg}$ mass are attached to the two opposite ends of a bar. The bar has negligible mass and a total length of $30.0\,\text{cm}$. The bar is in equilibrium when it is supported by a pivot located $20.0\,\text{cm}$ from the unknown mass, as shown. Determine the unknown mass.

Turning effects of forces

A wooden block with density $\rho_w$ has side lengths of $a$. It is immersed in a liquid whose density is $\rho_L$. The upper face of the block lies at a depth $h$ beneath the liquid surface. The acceleration of free fall is $g$. What upthrust does the liquid exert on the block?

Density and pressure

A technical article on diesel engines gives the energy available from diesel fuel in two forms: $41.8\,\text{MJ kg}^{-1}$ and $34.9\,\text{GJ m}^{-3}$. What is the density of diesel fuel?

Density and pressure

What does the term efficiency of a system mean?

Energy conservation

A car weighing $15\,000\,\text{N}$ is travelling on a horizontal road. At a particular moment, the thrust force from the engine on the car is $12\,000\,\text{N}$ and the resistive force on the car is $3000\,\text{N}$. The car's velocity at this instant is $24\,\text{m s}^{-1}$. Calculate the power output from the engine.

Energy conservation

The diagram illustrates how a quantity $y$ changes with a quantity $x$ for objects in a uniform gravitational field. What might $x$ and $y$ represent?

Gravitational potential energy and kinetic energy

Which list of unit prefixes reduces in magnitude from left to right?

SI units

A steel wire measures $300\,\text{cm}$ in length and has a cross-sectional area of $0.50\,\text{mm}^2$. Its Young modulus is $2.0 \times 10^{11}\,\text{Pa}$. One end of the wire is fastened to a fixed point, and a load of $10\,\text{N}$ is suspended from the other end. The wire follows Hooke’s law. Determine the extension of the wire.

Stress and strain

The extension of a copper wire is recorded for several different forces acting on the wire. A graph is drawn to illustrate how the force on the wire changes with extension. The greatest force is applied at point P. Which statement must be true?

Elastic and plastic behaviour

The way in which the displacement $y$ of a transverse wave on a rope varies with distance $x$ is shown at time $t = 0$. The wave has frequency $0.5\,\text{Hz}$. A point P on the rope is labelled. The diagram shows P in its initial position and also four possible new positions. What is the position of P at time $t = 1\,\text{s}$?

Progressive waves

A microphone that detects sound of constant frequency is linked to a cathode-ray oscilloscope (CRO). The trace displayed on the CRO screen is shown. Which property of the sound wave can be measured using only the information from the CRO?

Progressive waves

A transverse wave and a longitudinal wave each move in the same direction along a long stretched spring. Which statement about these two kinds of wave is not correct?

Transverse and longitudinal waves

A man beside a train at rest detects a sound with frequency $400\ \text{Hz}$ produced by the train’s horn. The train then travels directly away from the man and sounds its horn while moving at $50\ \text{m s}^{-1}$. The speed of sound in air is $340\ \text{m s}^{-1}$. What is the difference between the frequencies of the sound heard by the man in the two situations?

Doppler effect for sound waves

Which list of electromagnetic-spectrum regions is arranged in order of increasing wavelength from left to right?

Electromagnetic spectrum

The principle of superposition states that a particular quantity is combined when two or more waves meet at a point. What is this quantity?

Interference

In a gas-filled tube of length $L$, one end is sealed by a piston, and a stationary sound wave is produced. By shifting the piston, the tube length can be changed. The tube length and the sound frequency are adjusted so that the stationary wave always contains two antinodes and two nodes, as shown. The graph illustrates how the frequency $f$ of the stationary sound wave varies with the tube length $L$. What is the speed of sound in the gas in the tube?

Stationary waves

The diagrams illustrate the diffraction of water waves in a ripple tank as they move through an opening between two barriers. Which diagram is the correct one?

Diffraction

The drag coefficient $C_d$ is a dimensionless quantity. It is used to compare the drag on different cars at different speeds. $C_d$ is given by the equation $C_d = \frac{2F}{v^n \rho A}$, where $F$ is the drag force on the car, $\rho$ is the density of the air, $A$ is the cross-sectional area of the car and $v$ is the speed of the car. Find the value of $n$.

SI units

A beam of light from a laser falls normally on a double slit. Interference fringes are observed on a screen positioned parallel to the double slit. The slit separation is $a$. The gap between the slits and the screen is $D$. The spacing between the centres of two neighbouring bright fringes is $x$. $D$ and $a$ are both reduced by half. What is the spacing between the centres of two neighbouring bright fringes after these changes?

Interference

A beam of light with wavelength $400\ \text{nm}$ strikes a diffraction grating normally, and the grating has $300$ lines per millimetre. After passing through the grating, the light forms a set of maxima seen on a semicircular screen, as shown. What is the total number of maxima visible on the screen?

The diffraction grating

Wires X and Y are both made from the same metal. The diameter of wire Y is 2 times the diameter of wire X. Wire X, wire Y and a battery are joined in series. What is the ratio $\dfrac{\text{average drift speed of free electrons in wire X}}{\text{average drift speed of free electrons in wire Y}}$?

Electric current

A resistor with resistance $R$ carries current $I$ when the potential difference (p.d.) across it is $V$. The resistor dissipates power $P$. If charge $Q$ passes through the resistor, work $W$ is done. Which of these relationships among the variables is not correct?

Potential difference and power

A fixed resistor and a filament lamp are connected in series to a power supply. The $I$-$V$ characteristics of both components are shown. The current in the fixed resistor is $0.34\,\text{A}$. What is the resistance of the filament lamp?

Resistance and resistivity

A lump of conducting putty (modelling clay) with constant resistivity is shaped into a cylinder. The resistance $R$ across its flat ends (shaded) is recorded. The same volume of putty is then reshaped into cylinders with different lengths $L$, and for each value of $L$ the resistance $R$ across the flat ends is measured. Which graph best shows how $R$ varies with $L$?

Resistance and resistivity

The diagram displays the symbol of a component that could be used in an electrical circuit. Which component does this circuit symbol represent?

Practical circuits

Which row gives the correct description of Kirchhoff's laws?

Kirchhoff's laws

A potential divider circuit is made by placing a battery with negligible internal resistance in series with two variable resistors, as illustrated. The variable resistors have resistances $R_x$ and $R_y$. $V_x$ is the potential difference (p.d.) across the variable resistor whose resistance is $R_x$. $R_x$ and $R_y$ are both altered at the same time. Which combination of changes must lead to $V_x$ increasing?

Potential dividers

An actinium nucleus has a nucleon number of $227$ and a proton number of $89$. It decays to produce a radium nucleus, with a $\beta^-$ particle and an $\alpha$-particle emitted during the decay. What nucleon number and proton number does this radium nucleus have?

Atoms, nuclei and radiation

A micrometer screw gauge is used to determine the diameter of a small, uniform steel sphere. The diameter is measured as $5.00\,\text{mm} \pm 0.01\,\text{mm}$. Using these values, what percentage uncertainty is there in the calculated volume of the sphere?

Errors and uncertainties

Which statement is incorrect?

Scalars and vectors

Forces with magnitudes $2\,\text{N}$, $4\,\text{N}$ and $7\,\text{N}$ are combined to give a resultant force. The three force magnitudes are fixed, although the forces can act in any direction within the same plane. Which magnitude is not a possible value for the resultant force?

Equilibrium of forces

Two projectiles, X and Y, are launched from the same point on level ground and reach the same maximum height, as shown. Projectile X is projected vertically upwards, whereas projectile Y is projected at an angle to the horizontal. Air resistance is negligible. Which statement is correct?

Equations of motion

A small glider travels along a horizontal air track, as illustrated. At each end of the air track, the glider undergoes a perfectly elastic collision with a fixed buffer. Between collisions, the glider moves with constant speed. Which graph shows how the velocity $v$ of the glider changes with time $t$ as it travels between the two buffers?

Equations of motion

A car speeds up from rest. The graph shows how the momentum of the car changes with time. What does the gradient of the graph at a specific time represent?

Momentum and Newton's laws of motion

A ball is released onto a horizontal surface and rebounds straight upwards. While the ball is touching the ground, the following forces are acting: • the weight $W$ of the ball • the contact force $P$ applied to the ground by the ball • the contact force $N$ applied to the ball by the ground. At the moment the ball is in contact with the ground, it is instantaneously at rest. At this instant, which relationship is correct?

Momentum and Newton's laws of motion