Feb/March 2024

Which row gives a physical quantity together with its base unit in the SI system?

SI units

A ball moves through a liquid at a steady speed. Three forces act on it: an upthrust, a drag force and its weight. The liquid has a uniform density. Which statement is correct?

Equilibrium of forces

A number of small solid cubes each have a mass of $1.0\,\text{kg}$ and edge lengths of $5.0\,\text{cm}$. These small cubes are arranged to make one large solid cube with edge lengths of $2.0\,\text{m}$. What is the weight of the large cube?

Density and pressure

A borehole that is $2000\,\text{m}$ deep has oil and water in it, as illustrated. At the base of the borehole, the pressure caused by the liquids is $17.5\,\text{MPa}$. The density of the oil is $830\,\text{kg m}^{-3}$ and the density of the water is $1000\,\text{kg m}^{-3}$. What is the depth $x$ of the oil?

Density and pressure

A rod is mounted so that it can turn about one end. At the start, the angle $\theta$ between the rod and the horizontal is $0^{\circ}$. The rod’s weight produces a moment $M$ about the pivot. The rod is then turned in a vertical plane so that the angle $\theta$ of the rod rises from $0^{\circ}$ to $180^{\circ}$. Which graph represents the way $M$ varies with $\theta$?

Turning effects of forces

A trapdoor with a hinge is kept shut in the horizontal position by means of a cable. There are three forces acting on the trapdoor: its weight $W$, the tension $T$ in the cable, and the force $H$ at the hinge. Which list shows these three forces in order of increasing magnitude?

Equilibrium of forces

How is force defined?

Momentum and Newton's laws of motion

A boat travels with constant velocity $v$ in still water. A constant drag force $F$ acts on the boat. What power is required by the boat to move through the water?

Energy conservation

The diagram depicts four forces acting on a circular disc. Each force has magnitude $F$. Two of the forces act vertically, while the other two forces act horizontally. All four forces lie in the same plane as the disc. No additional forces act on the disc. The disc has diameter $d$. Which statement is correct?

Turning effects of forces

A ball is launched from level ground into the air and moves along the trajectory shown in the diagram. At points $Q$, $R$, $S$ and $T$, the ball has kinetic energies $E_Q$, $E_R$, $E_S$ and $E_T$ respectively. The diagram shows the height above the ground of each of these four points. Air resistance may be ignored. Which difference between the kinetic energies is the smallest?

Gravitational potential energy and kinetic energy

The battery in a small tablet computer starts out uncharged. It is linked to a constant $10\,\text{W}$ power supply for $2.0$ hours in order to charge the battery. The charging process has an efficiency of $80\%$. What amount of energy is stored in the battery?

Energy conservation

A car with mass $850\text{ kg}$ is moving along a straight horizontal path. The diagram shows two horizontal forces acting on the car in opposite directions. One force has magnitude $1200\text{ N}$, while the other has magnitude $1600\text{ N}$. What is the magnitude of the car’s acceleration?

Momentum and Newton's laws of motion

A firework that is initially at rest detonates and breaks into two fragments, which then travel horizontally in opposite directions. The explosion transfers a total kinetic energy of $E$ to the fragments. One fragment has mass $m$ and the other has mass $2m$. What is the speed of the fragment of mass $m$ immediately after the explosion?

Linear momentum and its conservation

A spring is attached at one end and stretched by a force $F$ applied to the opposite end. Its extension is $x$ and its elastic potential energy is $E_p$. The spring constant is $k$. The spring follows Hooke’s law. Which relationship is correct for this spring?

Elastic and plastic behaviour

A force-extension graph is obtained for a metal wire. What does the limit of proportionality of the wire describe?

Elastic and plastic behaviour

A spring has a spring constant of $6.0\,\text{N cm}^{-1}$. It is connected to a second spring with a spring constant of $4.0\,\text{N cm}^{-1}$. An $80\,\text{N}$ load is hung from this composite spring. What is the extension of the composite spring?

Elastic and plastic behaviour

Blue whales emit sound waves with frequencies from $10\,\text{Hz}$ to $40\,\text{Hz}$. In seawater, sound travels at approximately $1.5\,\text{km s}^{-1}$. Calculate the approximate range of wavelengths of the sound waves emitted by blue whales.

Progressive waves

A microphone picks up a sound wave, and it is shown on the screen of a cathode-ray oscilloscope (CRO). The wave has a frequency of $2.5\,\text{kHz}$. What is the time-base setting of the CRO?

Practical circuits

A source of sound waves that has a constant frequency is moving towards an observer who is stationary. The observer compares the sound waves reaching the observer’s position with the waves produced by the source of sound. What is detected by the observer?

Doppler effect for sound waves

Which sort of wave is unable to be polarised?

Polarisation

A light beam has power $P$ and a cross-sectional area of $A$. The wave amplitude in the beam is $X$. The beam is then altered so that its frequency stays the same, but its amplitude becomes $4X$ and its cross-sectional area decreases to $\frac{A}{3}$. What is the power of this new beam?

Progressive waves

A single signal generator is linked to two loudspeakers, and it outputs one frequency. The loudspeakers are arranged facing one another so that a stationary sound wave is formed in the space between them. A microphone, connected to a cathode-ray oscilloscope (CRO), is placed between the two loudspeakers. The microphone is then moved along the straight line joining the loudspeakers. As the microphone is moved, the CRO trace shows 5 maximum amplitudes. The microphone travels a distance of $2.0\,\text{m}$ from the position giving the first maximum to the position giving the fifth maximum. What is the wavelength of the sound wave?

Stationary waves

An object of mass $m$ hangs from a fixed point by means of a spring. The spring constant is $k$. The object is made to undergo vertical oscillations with period $T$. Which equation for $T$ is homogeneous with respect to base units?

Physical quantities

Two wave sources emit coherent waves. Which condition has to be satisfied for these waves to be coherent?

Interference

A student carries out an experiment on double-slit interference. To illuminate a double slit, the student uses laser light with a single wavelength, and an interference fringe pattern is seen on the screen. The student observes that the fringes are very closely spaced. What could the student reduce to make the fringes farther apart on the screen?

Interference

How are potential difference (p.d.) and electromotive force (e.m.f.) defined in terms of energy transfer $W$ and charge $q$?

Potential difference and power

The diagram represents a network made up of three resistors. What is the total resistance of the network between terminal $X$ and terminal $Y$?

Resistance and resistivity

A resistor dissipates $25\,\text{W}$ of power when the potential difference (p.d.) across it is $4.0\,\text{V}$. What is the resistance of this resistor?

Potential difference and power

The diagram represents a cell with internal resistance arranged in parallel with a fixed resistor and a variable resistor. The resistance of the variable resistor is reduced. What happens to the potential difference $V$ across the variable resistor and the current $I$ through the variable resistor?

Practical circuits

In a vacuum, a radioactive source emits a beam of $\alpha$-particles. The mean current due to the $\alpha$-particles in the beam is $1.5 \times 10^{-9}\,\text{A}$. The beam strikes a metal target. What is the mean number of $\alpha$-particles reaching the metal target in a time of $3.0\,\text{s}$?

Electric current

The charge carriers in a metal wire are free electrons. Which statement about the charge on each free electron is correct?

Electric current

Which quark flavours carry charge $+\frac{2}{3}e$?

Fundamental particles

A nucleus of an element that is unstable decays by releasing either an $\alpha$-particle or a $\beta^-$-particle, forming a nucleus of another element. That nucleus is unstable too and releases an $\alpha$-particle or a $\beta^-$-particle. This sequence carries on until an isotope of the original element is formed. What is the smallest possible number of these particles emitted?

Atoms, nuclei and radiation

A body with constant mass starts from rest at point $P$. It then travels away from point $P$ with constant acceleration. Which statement describes the resultant force acting on the body while it is moving?

Momentum and Newton's laws of motion

A nucleus of carbon-10, $^{10}_{6}\text{C}$, undergoes beta-emission and is transformed into a nucleus of boron-10, $^{10}_{5}\text{B}$. For this decay process, what change happens to a nucleon, and how does the quark composition of the nucleon change?

Fundamental particles

A projectile is fired at an angle of $25^{\circ}$ above the horizontal with a horizontal velocity component of $13\text{ m s}^{-1}$. What is the vertical component of the projectile’s velocity at the moment it is launched?

Scalars and vectors

A ball is let go from rest at position $X$ at time zero. At $1.0\text{ s}$, it undergoes an inelastic bounce off a horizontal surface and then rises, arriving at the highest point of its first rebound at $1.5\text{ s}$. What is the ball's total displacement from its starting position $X$ at $1.5\text{ s}$?

Equations of motion

What does acceleration mean?

Equations of motion

Two balls P and Q, with equal mass, are travelling in a straight line towards each other, as illustrated. Ball P has a velocity of $1.30\,\text{m s}^{-1}$ to the right. Ball Q has a velocity of $0.50\,\text{m s}^{-1}$ to the left. P and Q collide. The collision is perfectly elastic, so the total momentum is conserved. Which diagram shows the correct motion of P and Q after the collision?

Linear momentum and its conservation

A basketball player throws a ball straight downwards at a speed of $2.4\,\text{m s}^{-1}$ from a height of $0.90\,\text{m}$. The effect of air resistance can be ignored. What speed does the ball have when it reaches the ground?

Equations of motion

Table 1.1 shows several SI quantities. Complete the table by placing a tick () in the rows that are SI base quantities.

SI units

Define the term acceleration.

Equations of motion

Wire X is a thin metal wire with diameter $1.2 \times 10^{-3}\,\text{m}$, and it is used to support a model planet, as illustrated in Fig. 3.1. Fig. 3.2 shows how the stress for wire X changes with strain.

Stress and strain

Nucleus P undergoes $\alpha$-decay, producing nucleus Q.

Atoms, nuclei and radiation

Using the direction of propagation of energy, state what is meant by a transverse wave.

Electromagnetic spectrum

(a) A single-frequency coherent visible light beam is directed normally at a double slit. A bright-and-dark interference fringe pattern appears on a screen, as shown in Fig. 6.1.

Interference

Define the term electric potential difference.

Practical circuits

State the name of the class (group) of fundamental particles that includes a neutrino.

Fundamental particles

Explain why the gravitational potential close to a point mass is negative.

Gravitational potential

The Sun’s surface temperature is $5780\,\text{K}$. Its luminosity is $3.85 \times 10^{26}\,\text{W}$.

Stellar radii

Using both kinetic energy and potential energy, explain the meaning of the internal energy of an ideal gas.

The first law of thermodynamics

A small object with mass $24\,\text{g}$ is resting on a platform. The platform is connected to an oscillator, as shown in Fig. 3.1, and the oscillator makes the platform move vertically up and down.

Energy in simple harmonic motion

Three capacitors are arranged as in Fig. 4.1. Find the total capacitance, in $\mu\text{F}$, of the three-capacitor network.

Discharging a capacitor

An object moves in a circle at constant speed. State the names of two quantities that change as the motion continues.

Force on a moving charge

Coil C is a small coil with 64 turns and a cross-sectional area of $0.71\,\text{cm}^2$. It sits inside a solenoid, as shown in Fig. 6.1. The centre of coil C lies on the solenoid’s central axis.

Electromagnetic induction

A photon carries an energy of $3.11 \times 10^{-19}\,\text{J}$. Calculate the momentum of the photon.

Photoelectric effect

State the definition of the binding energy of a nucleus.

Mass defect and nuclear binding energy

Electrons in a vacuum are accelerated by a potential difference of $84\,\text{kV}$. They then collide with a metal target and X-rays are produced. Calculate the minimum wavelength of the X-rays that are produced.

Production and use of ultrasound