A Level Physics 9702 Paper 42, May/June 2026

With reference to velocity and acceleration, describe uniform circular motion.

An aircraft is travelling in a horizontal circle of radius $7200\text{ m}$ at a speed of $180{\text{ ms}}^{-1}$, as shown in the view from above in Figure 1.1. In order to move in a circle, the aircraft has to tilt its wings so that the lift force from the wings is not vertical, as shown in the view from behind in Figure 1.2. With reference to the forces acting on the aircraft, explain why the circular motion of the aircraft requires the lift force to be in the direction shown rather than vertically upwards.

On Figure 1.2, draw an arrow from the aircraft to represent the direction of the resultant force on the aircraft.

Calculate the centripetal acceleration of the aircraft. $$\text{acceleration}=\text{................................................ }{\text{ms}}^{-2}$$

Determine the angle $\theta$ at which the aircraft is tilted. Explain your reasoning. $$\theta ={\text{....................................................... }}^{\circ }$$

Define gravitational field at a point.

Figure 2.1 shows a horizontal section through a small piece of ground at the Earth's surface and the air at a small distance above it. On Figure 2.1, draw four field lines to represent the gravitational field of the Earth in the air above the ground.

The Earth may be considered to be an isolated uniform sphere of radius $6.37\times {10}^6\text{ m}$. By considering the gravitational field strength at the Earth's surface, calculate a value for the mass of the Earth. Give your answer to three significant figures. $$\text{mass}=\text{.................................................... kg}$$

Determine, to three significant figures, the gravitational potential at the Earth's surface. Give a unit with your answer. $$\text{gravitational potential}=\text{.................................. unit ...............}$$

A satellite of mass $96.0\text{ kg}$ is in circular orbit at a height of $1.93\times {10}^6\text{ m}$ above the Earth's surface. Determine the gravitational potential energy of the satellite. $$\text{gravitational potential energy}=\text{...................................................... J}$$

Define specific heat capacity.

A sample of an ideal gas contains $6.00\times {10}^{23}\text{ molecules}$, each of mass $6.64\times {10}^{-27}\text{ kg}$. The gas is at a pressure of $1.01\times {10}^5\text{ Pa}$. It has an initial volume of $0.0243{\text{ m}}^3$, an initial internal energy of $3676\text{ J}$ and an initial temperature of $296\text{ K}$. The gas is now cooled at constant pressure so that its volume becomes $80\mathrm{\%}$ of the initial volume. Show that the magnitude of the work done on the gas is $491\text{ J}$.

Explain whether the work done on the gas is positive or negative.

Explain why the increase in internal energy of the gas is $-735\text{ J}$.

Determine the thermal energy $Q$ transferred to the gas. $$Q=\text{...................................................... J}$$

Calculate a value for the specific heat capacity $c$ of the gas for this change. $$c={\text{......................................... Jkg}}^{-1}{\text{K}}^{-1}$$

The gas in 3(b) is now heated at constant volume so that its temperature returns to $296\text{ K}$. Use the first law of thermodynamics to explain, without calculation, whether the specific heat capacity for this change is less than, the same as, or greater than the answer in 3(b)(v).

State the two assumptions of the kinetic theory of gases that relate to collisions of particles with each other and with the walls of the container of the gas. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ...................................................................................................................................................

A single particle of an ideal gas has mass $m$. The particle is moving at speed $u$ in a cubic box of side length $L$, as shown in Figure 4.1. The particle is moving in a direction that is perpendicular to the two shaded faces, continually rebounding from one face and then the other. Determine an expression, in terms of some or all of $m$, $u$ and $L$, for: the magnitude of the change in momentum of the particle during each collision with a shaded face $$\text{change in momentum}=\text{.........................................................}$$

the time taken between consecutive collisions of the particle with one of the shaded faces $$\text{time}=\text{.........................................................}$$

the mean force exerted on the particle by one of the shaded faces $$\text{mean force}=\text{.........................................................}$$

the mean pressure $p$ exerted over the area of each of the shaded faces by the particle. Explain your reasoning. $$p=\text{.........................................................}$$

An ideal gas consists of $N$ particles moving in many different directions with a mean-square speed of $⟨c^2⟩$. Explain how the equation in 4(b)(iv) is modified to arrive at the more general equation $$pV=\frac{1}{3}Nm⟨c^2⟩$$ where $V$ is the volume of the gas.

Show that the angular frequency of the oscillations is $3.7\text{ rad}{\text{ s}}^{-1}$.

State what is meant by the amplitude of the oscillations.

Calculate the amplitude of the oscillations. $$\text{amplitude}=\text{..................................................... m}$$

On Figure 5.2, sketch the variation of the kinetic energy $E_K$ of the block with displacement $x$ from the equilibrium position for one complete oscillation of the block. Add a suitable scale to the $x$-axis.

Define electric potential at a point.

An isolated conducting sphere of radius $R$ is in a vacuum. The sphere has a charge of $+Q$ distributed around its surface, as illustrated in Figure 6.1. State an expression, in terms of $R$ and $Q$, for the magnitude $V_0$ of the electric potential at the surface of the sphere. Identify any other symbols that you use. $$V_0=\text{.........................................................}$$

On Figure 6.2, sketch the variation of the electric potential $V$ at distance $x$ from the centre of the sphere between $x=R$ and $x=3R$.

The dome of an electrostatic generator, called a Van de Graaff generator, may be considered to be a conducting sphere of radius $11.9\text{ cm}$. The dome is charged so that the electric potential at its surface is $-4.80\times {10}^4\text{ V}$. Calculate the charge on the surface of the dome. $$\text{charge}=\text{..................................................... C}$$

Explain why the dome acts as a capacitor.

Calculate the capacitance of the dome. Give a unit with your answer. $$\text{capacitance}=\text{.................................. unit ...............}$$

Determine the energy stored by the dome. $$\text{energy}=\text{...................................................... J}$$

Using the letters P, Q, R, S, W, X, Y and Z, identify the faces of the slice between which the Hall voltage is induced. .............................................................. and ..............................................................

The magnitude of the Hall voltage in Figure 7.1 is given by the equation $$V_H=\frac{BI}{nqt}\mathrm{.}$$ State the meanings of the symbols $n$, $q$ and $t$ in this equation. $n$ ........................................................................................................................................ $q$ ......................................................................................................................................... $t$ .........................................................................................................................................

Explain the origin of the Hall voltage.

Identify which of the faces in 7(a)(i) is at the higher potential. Explain your reasoning.

State the name of the component in the circuit that produces the rectification.

State the name of the component in the circuit that produces the smoothing.

Determine the peak value of $V_{\text{IN}}$. $$\text{peak value of }{V}_{\text{IN}}=\text{...................................................... V}$$

Determine the period of $V_{\text{IN}}$. $$\text{period of }{V}_{\text{IN}}=\text{...................................................... s}$$

Apart from the peak value and period of $V_{\text{IN}}$, determine three other conclusions that can be drawn from Figure 8.1 and Figure 8.2 about the input and output voltages and about the circuit. The conclusions may be qualitative or quantitative. Use the space for any working. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ................................................................................................................................................... 3 ................................................................................................................................................ ...................................................................................................................................................

State what is meant by the de Broglie wavelength.

Complete Table 9.1 to identify experimental evidence for the wave nature and the particulate nature of matter and of electromagnetic radiation. Table 9.1

An electron in a vacuum is accelerated from rest by a potential difference (p.d.) of $3.5\text{ kV}$. For the accelerated electron, calculate the speed $$\text{speed}={\text{................................................ ms}}^{-1}$$

the de Broglie wavelength. $$\text{wavelength}=\text{..................................................... m}$$

Define the binding energy of a nucleus.

A star emits radiation that is produced in a series of nuclear reactions that form helium from hydrogen. The reactions may be summarised by the overall equation $$4{}_1^1\text{H}\to {}_2^4\text{He}+2{}_1^0\text{X}$$ where X is a particle that has no binding energy. All of the radiation emitted by the star is produced by this series of nuclear reactions. The mass defect of the ${}_2^4\text{He}$ nuclide is $0.030377\text{ u}$, where $\text{u}$ is the unified atomic mass unit. State the name of particle X.

Show that the binding energy of the ${}_2^4\text{He}$ nuclide is $4.54\times {10}^{-12}\text{ J}$.

The star in 10(b) has a luminosity of $7.98\times {10}^{27}\text{ W}$. An observer on the Earth detects radiation from this star at a distance away of $8.15\times {10}^{16}\text{ m}$. Calculate the radiant flux intensity $F$ detected by the observer. $$F={\text{.............................................. Wm}}^{-2}$$

The mass of hydrogen in the star decreases continuously as a result of the series of nuclear reactions. Determine the rate of decrease of mass of hydrogen in the star. $$\text{rate of decrease of mass}={\text{............................................... kgs}}^{-1}$$