A Level Physics 9702 Paper 42, May/June 2024

Define the radian.

A circular metal disc spins horizontally about a vertical axis, as shown in Fig. 1.1. A piece of modelling clay is attached to the disc. For the instant when the piece of modelling clay is in the position shown, draw on Fig. 1.1: an arrow, labelled V, showing the direction of the velocity of the modelling clay

an arrow, labelled A, showing the direction of the acceleration of the modelling clay.

The metal disc in Fig. 1.1 has a radius of $9.3\text{ cm}$. The centre of gravity of the modelling clay is $1.2\text{ cm}$ from the rim of the disc and moves with a speed of $0.68{\text{ m s}}^{-1}$. Calculate the angular speed $\omega$ of the disc. $$\omega =\text{..............................................}{\text{ rad s}}^{-1}$$

Calculate the acceleration $a$ of the centre of gravity of the modelling clay. $$a=\text{................................................}{\text{ m s}}^{-2}$$

A second piece of modelling clay is attached to the disc in the position shown in Fig. 1.2. The second piece of modelling clay has a larger mass than the first piece. By placing one tick ($\mathrm{✓}$) in each row, complete Table 1.1 to show how the quantities indicated compare for the two pieces of modelling clay. Table 1.1

With reference to thermal energy, state what is meant by two objects being in thermal equilibrium.

Two cylinders X and Y each contain a sample of an ideal gas. The samples are in thermal equilibrium with each other. X has a volume of $0.0260{\text{ m}}^3$ and contains $0.740\text{ mol}$ of gas at a pressure of $1.20\times {10}^5\text{ Pa}$. Y has a volume of $0.0430{\text{ m}}^3$ and contains gas at a pressure of $2.90\times {10}^5\text{ Pa}$. Data for the two cylinders are shown in Fig. 2.1. Show that the temperature of the gas in X is $234{}^{\circ }\text{C}$.

Determine the number $N$ of molecules of the gas in Y. Explain your reasoning. $$N=\text{.........................................................}$$

The gas in X consists of molecules that each have a mass that is four times the mass of a molecule of the gas in Y. Explain how the root-mean-square (r.m.s.) speed of the molecules in X compares with the r.m.s. speed of the molecules in Y.

State what is meant by the internal energy of a system.

With reference to molecular kinetic and potential energies, describe and explain how the internal energy of the system changes when: a gas is heated at constant volume so that its temperature increases

With reference to molecular kinetic and potential energies, describe and explain how the internal energy of the system changes when: a wire is stretched within its elastic limit at constant temperature.

Explain how Fig. 4.2 shows that the oscillations of the block are simple harmonic.

Deduce expressions, in terms of some or all of $m$, $A$ and $Y$, for: the angular frequency $\omega$ of the oscillations $$\omega =\text{.........................................................}$$

Deduce expressions, in terms of some or all of $m$, $A$ and $Y$, for: the maximum speed $v_0$ of the oscillations $$v_0=\text{.........................................................}$$

Deduce expressions, in terms of some or all of $m$, $A$ and $Y$, for: the energy $E$ of the oscillations. $$E=\text{.........................................................}$$

The period of the oscillations is $0.75\text{ s}$ and the value of $3Y$ is $1.8\text{ cm}$. Determine an expression for $x$ in terms of time $t$, where $x$ is in $\text{cm}$ and $t$ is in seconds. $$x=\text{.........................................................}$$

Define electric potential at a point.

Two isolated charged metal spheres X and Y are near to each other in a vacuum. The centres of the spheres are $1.2\text{ m}$ apart, as shown in Fig. 5.1. Point P is on the line joining the centres of spheres X and Y and is at a variable distance $x$ from the centre of X. Fig. 5.2 shows the variation with $x$ of the total electric potential $V$ due to the two spheres. State three conclusions that may be drawn about the spheres from Fig. 5.2. The conclusions may be qualitative or quantitative. 1 ................................................................................................................................ ................................................................................................................................... 2 ................................................................................................................................ ................................................................................................................................... 3 ................................................................................................................................ ...................................................................................................................................

A proton is held at rest on the line joining the centres of the spheres in (b) at the position where $x=0.60\text{ m}$. The proton is released. Describe and explain, without calculation, the subsequent motion of the proton.

Two capacitors X and Y are connected in series to a power supply of voltage $V$, as shown in Fig. 6.1. The capacitance of X is $C_{\mathrm{X}}$ and the capacitance of Y is $C_{\mathrm{Y}}$. Derive an expression, in terms of $C_{\mathrm{X}}$ and $C_{\mathrm{Y}}$, for the combined capacitance $C_{\mathrm{T}}$ of the capacitors in this circuit. Explain your reasoning.

Two capacitors P and Q are connected in parallel to a power supply of voltage $V$. The capacitance of P is $200\mu \text{F}$. The capacitance $C_{\mathrm{Q}}$ of Q can be varied between $0$ and $400\mu \text{F}$. When $C_{\mathrm{Q}}=0$, the total energy stored in the capacitors is $2.5\text{ mJ}$. Show that the supply voltage $V$ is $5.0\text{ V}$.

Calculate the total energy, in $\text{mJ}$, stored in the capacitors when $C_{\mathrm{Q}}$ has its maximum value. $$\text{total energy}=\text{................................................... mJ}$$

On Fig. 6.2, sketch the variation of the total energy $E$ stored in the capacitors with $C_{\mathrm{Q}}$, as $C_{\mathrm{Q}}$ varies from $0$ to $400\mu \text{F}$.

State Faraday’s law of electromagnetic induction.

Fig. 7.1 shows a coil at rest in a uniform magnetic field that is parallel to the axis of the coil. The coil is connected to a centre-zero voltmeter. The flux density $B$ of the uniform magnetic field varies with time $t$ as shown in Fig. 7.2. The coil consists of $340$ turns, each of cross-sectional area $3.2\times {10}^{-4}{\text{ m}}^2$. Calculate the maximum magnetic flux through one turn of the coil. $$\text{maximum magnetic flux}=\text{................................................... Wb}$$

Determine the maximum rate of change of magnetic flux linkage in the coil. $$\text{maximum rate of change of flux linkage}=\text{.............................................}{\text{ Wb s}}^{-1}$$

State the maximum electromotive force (e.m.f.) $V_0$ induced across the coil. $$V_0=\text{...................................................... V}$$

On Fig. 7.3, sketch the variation of the e.m.f. $V$ induced across the coil with $t$ from $t=0$ to $t=6.0\text{ ms}$.

The variation of $V$ with $t$ can be described by $$V=A\sin Bt$$ where $A$ and $B$ are constants. Determine the values of $A$ and $B$. Give units with your answers. $$A=\text{.......................................unit ................}$$ $$B=\text{.......................................unit ................}$$

Explain how the positions of the lines in the emission spectrum seen by an observer on the Earth differ from the positions shown in Fig. 8.1.

On Fig. 8.1, draw the three lines in possible positions in the spectrum seen by the observer.

The lines in Fig. 8.1 correspond to electron transitions down to the energy level $-3.40\text{ eV}$. One of the lines represents emitted radiation of wavelength $488\text{ nm}$. Calculate the energy of a photon of this radiation. $$\text{photon energy}=\text{...................................................... J}$$

Determine the energy, in $\text{eV}$, of the energy level from which the electron transition originates to cause the emission of this radiation. $$\text{energy level}=\text{.................................................... eV}$$

Determine the wavelength, in $\text{nm}$, of this radiation as detected by the observer on the Earth. $$\text{wavelength}=\text{................................................... nm}$$

A value for the Hubble constant is $2.3\times {10}^{-18}{\text{ s}}^{-1}$. Determine the distance of the galaxy from the Earth. $$\text{distance}=\text{..................................................... m}$$

State what is meant by the binding energy of a nucleus.

Table 9.1 shows the masses of two sub-atomic particles and a polonium-212 (${}_{84}^{212}\text{Po}$) nucleus. Table 9.1

For the polonium-212 nucleus, determine: the mass defect $\mathrm{\Delta }m$, in $\text{kg}$ $$\mathrm{\Delta }m=\text{.................................................... kg}$$

For the polonium-212 nucleus, determine: the binding energy $$\text{binding energy}=\text{...................................................... J}$$

For the polonium-212 nucleus, determine: the binding energy per nucleon. $$\text{binding energy per nucleon}=\text{...................................................... J}$$

On Fig. 9.1, sketch the variation with nucleon number $A$ of binding energy per nucleon for values of $A$ from 1 to 250.

On your line in Fig. 9.1, draw an X to show the approximate position of polonium-212.

Polonium-212 is radioactive and undergoes alpha-decay. Suggest and explain, with reference to Fig. 9.1, why the alpha-decay of polonium-212 results in a release of energy.

Describe how reflected ultrasound pulses may be used to obtain diagnostic information about internal structures.

Define specific acoustic impedance of a medium.

Table 10.1 shows some data for water and for glass. Table 10.1

Determine the intensity reflection coefficient for ultrasound that is incident on a water–glass boundary. $$\text{intensity reflection coefficient}=\text{.........................................................}$$