A Level Physics 9702 Paper 42, Oct/Nov 2025

Show that the radius of the circle around which Cambridge moves is $3.90\times {10}^6\text{ m}$.

Calculate the speed at which Cambridge moves around the circle. speed = ................................................ ${\text{ms}}^{-1}$

A student of mass $58.6\text{ kg}$ stands on horizontal ground in Cambridge. Determine the magnitude of the resultant force that acts to cause the circular motion of the student. resultant force = ..................................................... N

On Fig. 1.2, draw an arrow to show the direction of the resultant force that acts on the student.

On Fig. 1.3, draw labelled arrows from the student to show the directions of the forces that act on the student to cause the resultant force in (b)(ii).

State Newton’s law of gravitation.

One of the basic assumptions of the kinetic theory of gases is that there are no forces exerted between the molecules of the gas except during collisions. State two other basic assumptions of the kinetic theory of gases. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ...................................................................................................................................................

Hydrogen gas consists of molecules that each have a mass of $3.34\times {10}^{-27}\text{ kg}$. Hydrogen may be considered to be an ideal gas. A spherical balloon contains $0.0160\text{ mol}$ of hydrogen gas at a temperature of $282\text{ K}$. At this temperature, the volume of gas in the balloon is $1.87\times {10}^{-4}{\text{ m}}^3$. Determine the pressure of the gas. pressure = .................................................... Pa

Estimate the average separation of the hydrogen molecules in the gas. average separation = ..................................................... m

Use your answer in (c)(ii) to calculate the average gravitational force between adjacent molecules in hydrogen gas. average force = ..................................................... N

By considering the weight of a molecule, suggest with a reason whether your answer in (d)(i) is consistent with the assumption of the kinetic theory of gases that there are no forces exerted between molecules.

State what is meant by two objects being in thermal equilibrium.

Fig. 3.1 shows a type of thermometer called a constant volume gas thermometer. The thermometer is used to determine the thermodynamic temperature $T$ of the gas in the glass bulb. The glass bulb is immersed in the environment for which the temperature is to be measured. The height of the movable glass tube is then adjusted so that the level of the liquid on the left-hand side aligns with the reference line X marked on the fixed glass tube. The reference line Y is marked on the side of the movable glass tube. The level of the liquid at Y is higher than at X as a result of the pressure of the gas in the glass bulb. The difference in height $\mathrm{\Delta }h$ between the liquid levels at X and Y is then measured using the scale. The thermodynamic temperature $T$ of the gas is directly proportional to the pressure of the gas. This pressure is directly proportional to $\mathrm{\Delta }h$. The value of $\mathrm{\Delta }h$ can be used to calculate the pressure of the gas. In order to do this, the gravitational field strength is used, along with a property of the liquid. State the property of the liquid that is used to calculate the pressure.

Before the measurement of $\mathrm{\Delta }h$ can be made, the glass bulb needs to reach thermal equilibrium with the environment for which the temperature is to be measured. State two disadvantages of using a constant volume gas thermometer to measure temperature. 1 ........................................................................................................................................ ........................................................................................................................................... 2 ........................................................................................................................................ ...........................................................................................................................................

Suggest one situation in which a constant volume gas thermometer would be an appropriate type of thermometer to choose for measuring temperature.

Level X aligns with $2.31\text{ cm}$ on the scale. At $0^{\circ }\text{C}$, level Y aligns with $8.69\text{ cm}$. At temperature $\theta$, level Y aligns with $7.83\text{ cm}$ on the scale. Determine a value for $\theta$ in ${}^{\circ }\text{C}$. $\theta$ = .................................................... ${}^{\circ }\text{C}$

State the first law of thermodynamics.

Use Fig. 4.1 and Fig. 4.2 to determine the general expression for the internal energy $U$ of the gas when it has pressure $p$ and volume $V$. $U$ = .........................................................

An ideal gas at thermodynamic temperature $T$ contains $N$ molecules. Use your answer in (b)(i) and the equation of state for an ideal gas to deduce an expression for $U$ in terms of $N$ and $T$. Identify any other symbols you use. $U$ = .........................................................

Determine expressions, in terms of $X$ and $Y$, for the work $W$ done on the gas during: change AB $W$ = .........................................................

change CD. $W$ = .........................................................

Use your answers in (c) and the first law of thermodynamics to determine an expression, in terms of $X$ and $Y$, for the net thermal energy $Q$ supplied to the gas during one full cycle ABCDA. Explain your reasoning. $Q$ = .........................................................

Fig. 5.2 shows the variation with $x$ of the acceleration $a$ of the ball. Explain how Fig. 5.2 shows that the oscillations of the ball are simple harmonic.

Determine the period $T$ of the oscillations. $T$ = ...................................................... s

At time $t=0$, when the displacement of the ball has its maximum value, the ball is immersed in a trough containing thick oil so that the ball is just below the surface of the oil. This results in the subsequent motion of the ball being heavily damped. State what is meant by damping.

On Fig. 5.3, sketch a possible variation of the displacement $x$ of the ball with $t$ between $t=0$ and $t=2T$.

Define electric field at a point.

An isolated conducting sphere in a vacuum has a capacitance of $69\text{ pF}$. The charge on the sphere is $+83\text{ pC}$. On Fig. 6.1, draw field lines to represent the electric field outside the sphere due to the charge on the sphere.

Calculate the electric potential at the surface of the sphere. electric potential = ...................................................... V

Determine the radius of the sphere. radius = ..................................................... m

Calculate the electric field strength $E$ at the surface of the sphere. Give a unit with your answer. $E$ = ...................................... unit ............

The sphere in (b) is discharged by connecting it to earth ($0\text{ V}$) through a resistor of resistance $120\text{ M}\mathrm{\Omega }$. Calculate the time taken for the charge to fall to $26\text{ pC}$. time = ...................................................... s

For the alternating voltage: show that the period is $0.050\text{ s}$

determine the root-mean-square (r.m.s.) voltage. r.m.s. voltage = ...................................................... V

On Fig. 7.1, sketch the variation of $V$ with $t$ for values of $t$ from $t=0$ to $t=100\text{ ms}$.

The alternating voltage is rectified to produce an output voltage across a load resistor $R$, as shown in Fig. 7.2. Fig. 7.3 shows the variation with $t$ of the power $P$ in the load resistor. State three conclusions that can be drawn from Fig. 7.3. The conclusions may be qualitative or quantitative. Use the space for any working. 1 ................................................................................................................................................ ................................................................................................................................................... 2 ................................................................................................................................................ ................................................................................................................................................... 3 ................................................................................................................................................ ...................................................................................................................................................

Use the photon model of electromagnetic radiation to explain how the existence of spectral lines in the emission spectrum provides evidence for discrete electron energy levels in the hydrogen atom.

The energy of the ground state (level $n=1$) in a hydrogen atom is $-13.6\text{ eV}$. Calculate the energy, in $\text{J}$, of the ground state. energy = ...................................................... J

Show that the energy difference between levels $n=1$ and $n=2$ is $10.2\text{ eV}$.

Complete Table 8.1 to show the energy differences from the ground state, and the energies of the levels up to $n=4$, in the hydrogen atom. Use the space for any working. Table 8.1

State what is meant by the mass defect of a nucleus.

The nuclear fusion reaction for the formation of helium-4 from deuterium is represented by $${}_1^2\text{H}{+}_1^2\text{H}{\to }_2^4\text{He}\mathrm{.}$$ Table 9.1 shows the masses of the nuclides involved in this reaction. Table 9.1 Calculate the energy released in the formation of $1.00\text{ mol}$ of helium-4. energy = ...................................................... J

The star Sirius has a radius of $1.19\times {10}^9\text{ m}$ and loses mass due to nuclear fusion at a rate of $1.09\times {10}^{11}\text{ kg}{\text{s}}^{-1}$. Assume that the power of the radiation emitted by the star is equal to the power released by this process. Determine a value for the luminosity of Sirius. Give a unit with your answer. luminosity = ..................................... unit ............

Use your answer in (c)(i) to determine the surface temperature of Sirius. surface temperature = ...................................................... K

Explain how cosmologists use standard candles to estimate the distance of a galaxy from the Earth.

State what is meant by contrast in an X-ray image.

X-rays of intensity $I_0$ are incident normally on a structure, as shown in Fig. 10.1. Material P has a linear attenuation coefficient of $0.35{\text{ cm}}^{-1}$. The X-rays emerging from the structure in region A have an intensity of $0.053I_0$. Show that the intensity of the X-rays emerging in region B is $0.13I_0$.

Determine the linear attenuation coefficient $\mu$ of material Q. $\mu$ = ................................................ ${\text{cm}}^{-1}$

Use the information in (b)(i) to suggest why the X-rays emerging from the structure form an image that has poor contrast.

Explain how X-rays are used in computed tomography (CT) scanning to produce a three-dimensional image of an internal structure.