A Level Physics 9702 Paper 23, Oct/Nov 2025

Define acceleration.

A rocket is launched vertically from the surface of the Earth. Fig. 1.1 shows the variation of the velocity of the rocket with time for the first $20\text{ s}$ after its launch. Determine the acceleration of the rocket.

Show that the height of the rocket above the surface of the Earth at a time of $20\text{ s}$ after launch is $3.2\text{ km}$.

The mass of the rocket in (b) is $2.9\times {10}^6\text{ kg}$. Assume that this mass remains constant. For this rocket, from launch to its height at a time of $20\text{ s}$ after launch: calculate the gain in gravitational potential energy $\mathrm{\Delta }{E}_{\text{P}}$

calculate the gain in kinetic energy $\mathrm{\Delta }{E}_{\text{K}}$

determine the average power output of the rocket engines. Assume that resistive forces are negligible.

Define pressure.

Explain how hydrostatic pressure results in an upthrust force acting on a solid object immersed in a liquid.

A small steel ball of radius $r$ and mass $m$ falls vertically at terminal speed $v$ through oil. The viscous drag force $D$ that acts on the ball is given by $$D=6\pi \eta rv$$ where $\eta$ is a property of the oil called its viscosity. On Fig. 2.1, draw labelled arrows from the ball to show the directions of the three forces that act on the ball as it falls.

Determine the SI base units of $\eta$.

The oil in (b) has a density of $920\text{ kg}{\text{ m}}^{-3}$ and a viscosity of $4.7$ in SI units. The steel ball has a mass of $2.4\times {10}^{-3}\text{ kg}$ and a radius of $4.2\times {10}^{-3}\text{ m}$. Show that the upthrust force acting on the ball is $2.8\times {10}^{-3}\text{ N}$.

Determine the terminal speed $v$ of the ball.

Define the Young modulus of a material.

State an expression, in terms of some or all of $L$, $A$, $E$ and $\rho$, for the resistance $R_0$ of the wire.

Show that the spring constant $k_0$ of the wire is given by $$k_0=\frac{EA}{L}$$.

The wire is stretched, within the limit of proportionality, by a tensile force $F$. Assume that any changes in the cross-sectional area of the wire are negligible. On Fig. 3.1, sketch the variation with$F$ of the resistance $R$ of the wire.

On Fig. 3.2, sketch the variation with $F$ of the spring constant $k$ of the wire.

Copper has a resistivity of $1.8\times {10}^{-8}\mathrm{\Omega }\text{ m}$ and a Young modulus of $1.3\times {10}^{11}\text{ Pa}$. A copper wire of diameter $1.6\text{ mm}$ has a resistance of $0.034\mathrm{\Omega }$. Show that the length of the wire is $3.8\text{ m}$.

Use the equation in (b)(ii) to determine the spring constant of the wire.

State what is meant by diffraction of a wave.

A beam of vertically polarised light of wavelength $540\text{ nm}$ is incident normally on a diffraction grating, as shown in Fig. 4.1. The diffraction grating has a line spacing of $5.0\times {10}^{-6}\text{ m}$. The light transmitted by the diffraction grating illuminates a circular screen. The diffraction grating is at the centre X of the circle. The central bright fringe is formed at point O on the screen and has intensity$I_0$. P is a point on the screen where the line XP is at a variable angle$\theta$ to the line XO. The intensity $I$ of light on the screen at P varies with $\theta$. Show that the angle$\theta$ at which the first-order bright fringe is formed is ${6.2}^{\circ }$.

Determine the value of $\theta$ at which the second-order bright fringe is formed.

On Fig. 4.2, sketch the variation of the intensity $I$ with $\theta$ for values of $\theta$ from $-{15}^{\circ }$ to $+{15}^{\circ }$.

A polarising filter is placed in the path of the light beam that is incident on the diffraction grating in Fig. 4.1. The transmission axis of the filter is at ${45}^{\circ }$ to the vertical. Suggest how the variation of intensity with $\theta$ for the light on the screen compares with the answer in (b)(iii).

State Kirchhoff’s first law.

Fig. 5.1 shows a circuit containing a thermistor T that has a negative temperature coefficient. The thermistor has resistance $R_0$ at a temperature of $0{}^{\circ }\text{C}$. On Fig. 5.2, sketch a possible variation of the resistance of the thermistor with temperature between $0{}^{\circ }\text{C}$ and $100{}^{\circ }\text{C}$.

With reference to the current in the cell, explain why the current in resistor R decreases with increasing temperature of the thermistor.

The electromotive force (e.m.f.) $E$ of the cell in Fig. 5.1 is $1.50\text{ V}$. The internal resistance $r$ of the cell is $0.12\mathrm{\Omega }$. Resistor R has a resistance of $6.00\mathrm{\Omega }$. At a particular temperature of the thermistor, the current in R is $0.200\text{ A}$. For this temperature of the thermistor, determine: the current in the cell

the resistance of the thermistor.

Determine the numbers of protons, neutrons and electrons in a neutral atom of tritium. number of protons = ............................................................... number of neutrons = ............................................................... number of electrons = ...............................................................

Draw a labelled diagram to represent a simple model of the arrangement of the protons, neutrons and electrons in a tritium atom.

Tritium is radioactive and undergoes ${\beta }^{-}$ decay to form an isotope of helium (He). Gamma radiation is not emitted during this decay. Complete the equation to represent the radioactive decay of tritium. $${}_1^3\text{H}\to {\dots }_{\dots }^{\dots }\text{He}+{\dots }_{\dots }^{\dots }\beta {+}_0^0\text{X}$$

State the name of particle X.

Determine the quark composition of a tritium nucleus.