Feb/March 2025

Which quantity counts as a scalar quantity?

Scalars and vectors

A solid is entirely beneath the surface of a liquid. A student finds the ratio $\frac{\text{upthrust acting on the object}}{\text{weight of the object}}$. Which one change would make this ratio twice as large?

Density and pressure

A shop sign with weight $75\,\text{N}$ is suspended from a frame fixed to a vertical wall. The frame is made up of a horizontal rod XY and a rod YZ, which makes an angle of $30^\circ$ to the horizontal. Rod XY is hinged to the wall at X and its length is $0.50\,\text{m}$. Take the weights of the rods to be negligible. What horizontal force does the wall exert on rod XY?

Turning effects of forces

A student measures quantities in order to work out the density of a liquid in a beaker. The liquid has a height of $0.20\,\text{m} \pm 2\%$ in the beaker. The beaker’s internal diameter is $0.05\,\text{m} \pm 3\%$. The liquid’s mass is $0.36\,\text{kg} \pm 10\%$. Determine the percentage uncertainty in the calculated density of the liquid.

Errors and uncertainties

The diagram represents a uniform plank XY with length $4.0\,\text{m}$ and weight $300\,\text{N}$. The plank is supported by fixed supports at both ends X and Y. A child whose weight is $600\,\text{N}$ is placed at different points on the plank. At end X, the support applies an upward force $F$ on the plank. What is the value of $F$ when the child is positioned at X and when the child is positioned at Y?

Equilibrium of forces

In deriving the equation shown, which relationship is applied? $\text{power} = \text{force} \times \text{velocity}$

Energy conservation

A block is let go from rest at the top of a slope that is inclined at an angle to the horizontal. As shown in the diagram, the slope has length $L$. No resistive forces act on the block. What is the block’s speed at the bottom of the slope?

Energy conservation

A skateboarder and her skateboard have a combined mass of $70\,\text{kg}$. By pushing against the ground with her foot, she produces a forward force $F$ of $25\,\text{N}$ on herself and the skateboard, as shown in the diagram. Before the skateboarder raises her foot away from the ground, the skateboarder and skateboard move forwards by $0.50\,\text{m}$. What is the work done by $F$ on the skateboarder and skateboard?

Energy conservation

Inside a hydroelectric power station, a turbine lies at a vertical depth of $30\,\text{m}$ below the surface of a large lake. Water flows through the turbine at a rate of $340\,\text{m}^3\,\text{per minute}$. The combined efficiency of the turbine and generator system is $90\%$. The density of water is $1000\,\text{kg m}^{-3}$. Calculate the useful power output of the power station?

Gravitational potential energy and kinetic energy

A projectile is projected at an angle of $45^\circ$ above the horizontal and has initial kinetic energy $E$. If air resistance is taken to be negligible, what is the projectile’s kinetic energy at its greatest height?

Energy conservation

A wire is stretched by a tensile force, and its deformation remains elastic. What does elastic deformation mean?

Elastic and plastic behaviour

How does a systematic error affect the measurement of a physical quantity?

Errors and uncertainties

A bolt experiences a tensile force, as illustrated. Its cross-section is circular. At end X, the diameter measures $2d$. At end Y, the diameter measures $d$. What is the value of the ratio $\dfrac{\text{stress at Y}}{\text{stress at X}}$?

Stress and strain

The graph illustrates how the force on a compression spring varies with the change in the spring’s length. A spring of this type is fitted at each corner of a horizontal square plate. Each spring is arranged with its axis vertical. Together, the four springs carry a total load of $160\ \text{N}$. Calculate the total elastic potential energy stored in the four springs.

Elastic and plastic behaviour

Which row correctly identifies the properties shared by all electromagnetic waves?

Electromagnetic spectrum

What is the approximate wavelength range in free space for infrared radiation?

Electromagnetic spectrum

The diagram illustrates a car moving from point X to point Y in a straight path at a steady speed between person P and person Q. As it moves, the car keeps its horn sounding all the time. The horn produces sound with a fixed frequency. Which of the following statements about the sounds heard by person P and person Q during the car’s movement are correct? 1. Person P hears a sound whose frequency increases. 2. Person Q hears a sound whose frequency decreases. 3. Person Q always hears a sound with a higher frequency than person P.

Doppler effect for sound waves

A progressive wave with frequency $300\ \text{Hz}$ moves at a speed of $600\ \text{m s}^{-1}$. Calculate the phase difference between two points on the wave separated by a distance of $0.50\ \text{m}$.

Progressive waves

A beam of polarised light with intensity $I$ falls normally on a polarising filter. The intensity of the transmitted light is $I$. The filter is then rotated about the normal axis through an angle $\theta$. The transmitted light now has intensity $0.75I$. What is the angle $\theta$?

Polarisation

Light waves originate from two sources. What condition is required for observable interference fringes to form?

Interference

The diagram represents a water wave in a shallow tank. The wave passes through a gap in a barrier, causing diffraction and spreading out. The wavelength of the wave is much less than the width of the gap. The wavelength of the wave and the width of the gap are each altered by a small amount. Which combination of changes must make the spreading due to diffraction larger?

Diffraction

A beam of light with wavelength $567\,\text{nm}$ falls perpendicularly on a diffraction grating. The grating contains $400$ lines per $\text{mm}$. Several diffraction maxima are seen on the far side of the grating. What is the angle between the second-order maximum and the third-order maximum?

The diffraction grating

A car experiences a constant resultant force of $300\,\text{N}$ and accelerates for $5.0\,\text{s}$. The way in which the car’s velocity, in $\text{cm s}^{-1}$, changes with time is shown. Find the mass of the car.

Momentum and Newton's laws of motion

Two cylindrical conductors, X and Y, are made of the same material. They have the same length, but the diameter of Y is smaller than that of X. X and Y are joined in series to a cell. Which row compares the number of charge carriers per unit time passing through X with that through Y, and also compares the average drift speed of the charge carriers in X with that in Y?

Electric current

A copper wire has a length of $6.4\,\text{m}$ and a resistance of $0.92\,\Omega$. The resistivity of copper is $1.8 \times 10^{-8}\,\Omega\,\text{m}$. What is the wire’s diameter?

Resistance and resistivity

A thermistor is joined to a cell with negligible internal resistance. Which graph shows how the power, $P$, dissipated in the thermistor changes with temperature?

Potential difference and power

A metal electrical conductor has a resistance of $5.6\,\text{k}\Omega$. A potential difference (p.d.) of $9.0\,\text{V}$ is applied across its two ends. How many electrons pass through a point in the conductor in one minute?

Electric current

Which circuit symbol is not used for an electric component intended to produce sound waves?

Practical circuits

The diagram depicts a circuit junction where three wires, P, Q and R, are connected. The currents in P and Q are $1\,\text{A}$ and $3\,\text{A}$ respectively, in the directions indicated. How much charge passes a fixed point in wire R during a time of $5\,\text{s}$?

Electric current

A cell with electromotive force (e.m.f.) $E$ and internal resistance $r$ is connected in series to a switch $S$ and an external resistor of resistance $R$. The potential difference (p.d.) across P and Q is $V$. Which statement is correct when $S$ is moved from open to closed?

Potential difference and power

How would you describe a baryon in general terms?

Fundamental particles

A nucleus that is at rest has nucleon number $A$. It decays by releasing a proton with speed $v$, producing a new nucleus with speed $u$. The proton and the new nucleus travel in opposite directions, moving away from each other. Which equation expresses $v$ in terms of $A$ and $u$?

Linear momentum and its conservation

What change occurs in the quark composition of a nucleus during $\beta^+$ decay?

Atoms, nuclei and radiation

An aircraft begins from rest on a runway and reaches a take-off speed of $85\,\text{km h}^{-1}$ over a distance of at most $1.20\,\text{km}$. What minimum constant acceleration is required for the aircraft?

Equations of motion

What charge, expressed in terms of the elementary charge $e$, does a charm quark carry?

Fundamental particles

A projectile is launched upward from level ground. It starts with an initial velocity of $20\,\text{m s}^{-1}$ at an angle of $45^{\circ}$ to the horizontal. Air resistance is negligible. Which statement gives the speed of the object from the moment it is fired until just before it lands on the ground again?

Equations of motion

What does a statement of the principle of conservation of momentum for a system say?

Linear momentum and its conservation

Objects P and Q make up an isolated system. Object P has mass $6.0\,\text{kg}$ and is travelling at a speed of $3.0\,\text{m s}^{-1}$. Object Q has mass $2.0\,\text{kg}$ and is travelling at a speed of $4.2\,\text{m s}^{-1}$ at an angle of $35^{\circ}$ to the path of P. Objects P and Q collide and remain stuck together. What is the magnitude of the component of the final momentum of the combined objects in the original direction of P?

Linear momentum and its conservation

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

Momentum and Newton's laws of motion

The diagram represents a child X with mass $20\,\text{kg}$ and a child Y with mass $15\,\text{kg}$ sitting on a uniform plank. The plank has a mass of $7.0\,\text{kg}$ and a pivot located at its midpoint. The plank is horizontal and is in equilibrium. Which statement about the weight of the plank is correct?

Turning effects of forces

Explain what the accuracy of a measured value means.

Errors and uncertainties

State the principle of moments in words.

Turning effects of forces

A truck R of mass $9400\,\text{kg}$ travels down a slope in a straight line with constant acceleration, as shown in Fig. 3.1. At point A the truck has speed $13\,\text{m s}^{-1}$ and at point B its speed is $22\,\text{m s}^{-1}$. The distance from A to B is $180\,\text{m}$.

Momentum and Newton's laws of motion

As shown in Fig. 4.1, a device with a microwave emitter and receiver is positioned in a vacuum in front of a large metal sheet. Line XY is at right angles to the metal sheet. The device sends out microwaves with frequency $6.3\,\text{GHz}$.

Stationary waves

A loudspeaker at rest produces sound with a constant frequency. A microphone is positioned close to the loudspeaker and linked to a cathode-ray oscilloscope (CRO). The trace displayed on the CRO screen is shown in Fig. 5.1. The CRO time-base is adjusted to $5.0 \times 10^{-4}\,\text{s cm}^{-1}$.

Doppler effect for sound waves

A copper wire $P$ with a cylindrical shape and length $0.24\,\text{m}$ is illustrated in Fig. 6.1. The current in the wire is $0.85\,\text{A}$. The resistance of the wire is $3.3\,\text{m}\Omega$. The total number of charge carriers, $N$, in the wire is $2.6 \times 10^{22}$. The resistivity of copper is $1.8 \times 10^{-8}\,\Omega\,\text{m}$.

Electric current

A nucleus Q that is isolated and stationary decays to nucleus R plus an $\alpha$-particle. The $\alpha$-particle has a speed of $1.5 \times 10^7\,\text{m s}^{-1}$.

Atoms, nuclei and radiation

A steel ball rests on the inner surface of a hollow circular cone. It travels in a horizontal circle at constant speed, as shown in Fig. 1.1. The side of the cone makes an angle of $52\degree$ to the horizontal. There is no friction between the ball and the cone.

Centripetal acceleration

State what the luminosity of a star means.

Stellar radii

The size of the gravitational potential at the surface of a planet of radius $R$ is $\phi$. Treat the planet as an isolated sphere. On Fig. 2.1, sketch how the gravitational potential varies with distance $x$ from the centre of the planet for $R \le x \le 4R$.

Gravitational potential

Cuboids P and Q, both made of metal, are in thermal contact with one another.

Kinetic theory of gases

A tiny crystal is set oscillating in simple harmonic motion. Figure 4.1 shows how the displacement $x$ of one face of the crystal from its equilibrium position changes with time $t$.

Production and use of ultrasound

A capacitor with capacitance $C_1$ is placed in series with another capacitor of capacitance $C_2$. Show that the combined capacitance $C$ of the two capacitors is given by $\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2}$.

Discharging a capacitor

A velocity selector is made by combining an electric field with a magnetic field. Charged particles, known as ions, enter the space between parallel plates where the electric and magnetic fields are uniform, as shown in Fig. 6.1.

Force on a moving charge

State Faraday’s law for electromagnetic induction.

Electromagnetic induction

State the meaning of a photon.

Energy and momentum of a photon

Polonium-193 $^{193}_{84}\text{Po}$ is an unstable nuclide. A nucleus of polonium-193 undergoes decay into a nucleus of lead-189 $^{189}_{82}\text{Pb}$ by emitting an alpha-particle.

Radioactive decay