9702 Physics November 2025 Question Paper 41

In terms of velocity and acceleration, describe uniform circular motion of an object.

Fig. 1.1 shows the view from above of a polystyrene ball undergoing horizontal circular motion of radius $R$.

Fig. 1.1

The ball is illuminated by parallel light so that a shadow of the ball forms on a screen placed on the opposite side of the ball from the light source.

The line joining points O and P is perpendicular to the screen.

The angular speed of the circular motion is $\omega$.

The ball in \textbf{(b)} is in the position shown in Fig. 1.1, such that line OB is at an angle $\theta$ to the line OP.

The circular motion of the ball in Fig. 1.1 has a diameter of $0.46\text{ m}$ and an angular speed of $1.9\text{ rad}\,\text{s}^{-1}$.

For the simple harmonic motion of the shadow of the ball in Fig. 1.1, calculate:

On Fig. 1.1, draw, and label with the letter A, the position of the shadow on the screen when the shadow has its maximum positive acceleration.

State \textbf{two} ways in which the first law of thermodynamics describes that the internal energy of a system may be changed.

1. \hrulefill
2. \hrulefill

Define gravitational field at a point.

Fig. 3.1 shows an isolated point mass of mass $M$.

Point P is at distance $x$ from the point mass.

Two identical isolated uniform spheres X and Y each have radius $R$. The centres of the spheres are separated by distance $L$, as shown in Fig. 3.3.

Point P lies on the line joining the centres of X and Y, and is at a variable displacement $x$ from the centre of sphere X. The gravitational field strength at the surface of each sphere is $g_0$.

On Fig. 3.4, sketch the variation with $x$ of the gravitational field $g$ at point P between $x = R$ and $x = L - R$.

State the value of absolute zero on:

A sample contains a fixed amount of gas. The gas has pressure $p$, volume $V$ and thermodynamic temperature $T$.

Fig. 4.1 shows the variation of $pV$ with $kT$ for the sample, where $k$ is the Boltzmann constant.

The root-mean-square (r.m.s.) speed of the molecules of the gas is $1900\text{ m}\,\text{s}^{-1}$ when $pV$ is equal to $270\text{ J}$.

Determine the mass, in u, of one molecule of the gas, where u is the unified atomic mass unit.

$\text{mass} = \hrulefill \text{ u}$

Define electric potential at a point.

A hydrogen atom may be considered to consist of a proton and an electron separated by a distance of $120\text{ pm}$, as shown in Fig. 5.1.

The two particles may be considered as point charges.

Point P lies on the line joining the electron and the proton and is at a variable distance $x$ from the proton.

Complete Table 6.1 to indicate how $Q_S$, $Q_1$ and $Q_2$ relate to each other, and how $V_S$, $V_1$ and $V_2$ relate to each other, for series and parallel connections of the capacitors to the supply.

\textbf{Table 6.1}

\begin{tabular}{|c|c|c|} \hline & relationship between charges & relationship between p.d.s \ \hline series & & \ \hline parallel & & \ \hline \end{tabular}

An isolated capacitor of capacitance $470\ \mu\text{F}$ stores $19\text{ mJ}$ of energy.

State Faraday’s law of electromagnetic induction.

An aircraft is flying horizontally at constant speed $v$ through the Earth’s magnetic field, as shown in Fig. 7.1.

At the location of the aircraft, the vertical component of the Earth’s magnetic field is $38\ \mu\text{T}$ towards the ground.

The distance between the wingtips P and Q of the aircraft is $68\text{ m}$.

As the aircraft moves through the magnetic field, an electromotive force (e.m.f.) of $0.54\text{ V}$ is induced between the wingtips P and Q.

State what is meant by a photon.

A stationary nucleus of uranium-238 ($^{238}_{92}\text{U}$) undergoes alpha decay to produce a nucleus of thorium-234 ($^{234}_{90}\text{Th}$). The kinetic energy of the emitted alpha particle is $4.200\text{ MeV}$. A gamma-ray photon is also emitted during the decay.

Assume that the rebound kinetic energy of the thorium nucleus is negligible.

Table 8.1 shows the masses of the nuclides involved in the decay reaction. The mass of the uranium-238 nuclide is missing.

\textbf{Table 8.1}

\begin{tabular}{|c|c|} \hline nuclide & nuclide mass/u \ \hline $^{4}_{2}\alpha$ & $4.000407$ \ \hline $^{234}_{90}\text{Th}$ & $233.915174$ \ \hline $^{238}_{92}\text{U}$ & \ \hline \end{tabular}

The total energy released in the decay of the nucleus of uranium-238 is $4.274\text{ MeV}$.

Gamma radiation emitted during the decay of a sample of uranium-238 has a single wavelength.

Nuclei of cobalt-60 ($^{60}_{27}\text{Co}$) decay by beta emission, and also emit gamma radiation in the process.

Suggest why there is \textbf{not} a single wavelength for the gamma radiation emitted during the decay of a sample of cobalt-60.

State Wien’s displacement law.

Fig. 9.1 shows the variation with $d^{-2}$ of the radiant flux intensity $F$ observed from a star X, where $d$ is the distance of the observer from the star. Fig. 9.2 shows the variation with wavelength $\lambda$ of the rates of emission $P$ of radiation by star X and the Sun.

The surface temperature of the Sun is $5770\text{ K}$.

State \textbf{three} conclusions about star X that can be drawn from this data. The conclusions may be qualitative or quantitative. Use the space for any working.

1. \hrulefill
2. \hrulefill
3. \hrulefill

Star X is in a galaxy that is moving away from the Earth.

Suggest, with a reason, how the line for star X in Fig. 9.2 would appear differently if it had been obtained from data measured on the Earth.

Define specific acoustic impedance.

Explain how ultrasound waves are detected by a piezoelectric crystal.

Table 10.1 shows the specific acoustic impedance $Z$ for body tissue, water and steel.

\begin{center} \textbf{Table 10.1}

\begin{tabular}{|c|c|} \hline material & $Z / \text{kg}\,\text{m}^{-2}\,\text{s}^{-1}$ \ \hline body tissue & $1.38 \times 10^6$ \ \hline water & $1.48 \times 10^6$ \ \hline steel & $4.04 \times 10^7$ \ \hline \end{tabular} \end{center}