A Level Physics 9702 Paper 42, May/June 2023

State Newton’s law of gravitation.

A satellite is in a circular orbit around a planet. The radius of the orbit is $R$ and the period of the orbit is $T$. The planet is a uniform sphere. Use Newton’s law of gravitation to show that $R$ and $T$ are related by $$4{\pi }^2{R}^3=GM{T}^2$$ where $M$ is the mass of the planet and $G$ is the gravitational constant.

The Earth may be considered to be a uniform sphere of mass $5.98\times {10}^{24}\text{ kg}$ and radius $6.37\times {10}^6\text{ m}$. A geostationary satellite is in orbit around the Earth. Use the expression in (b) to determine the height of the satellite above the Earth’s surface.

Another satellite is in a circular orbit around the Earth with the same orbital radius and period as the satellite in (c). Calculate the angular speed of the satellite in this orbit. Give a unit with your answer.

Despite having the same orbital period, the orbit of this satellite is not geostationary. Suggest two ways in which the orbit of this satellite could be different from the orbit of the satellite in (c).

State what is meant by an ideal gas.

State the temperature, in degrees Celsius, of absolute zero.

A sealed vessel contains a mass of $0.0424\text{ kg}$ of an ideal gas at $227{}^{\circ }\text{C}$. The pressure of the gas is $1.37\times {10}^5\text{ Pa}$ and the volume of the gas is $0.640{\text{ m}}^3$. Calculate: the number of molecules of the gas in the vessel

Calculate: the mass of one molecule of the gas

Calculate: the root-mean-square (r.m.s.) speed $v$ of the molecules of the gas.

The gas in (b) is now cooled gradually to absolute zero. On Fig. 2.1, sketch the variation with thermodynamic temperature $T$ of the r.m.s. speed of the molecules of the gas.

State the first law of thermodynamics. Identify the meaning of any symbols that you use.

The state of an ideal gas is continuously changed according to the cycle ABCDA shown in Fig. 3.1. Complete Table 3.1 for the changes A to B and B to C by placing two ticks (✓) in each row.

Use the first law of thermodynamics to describe and explain the energy transfers associated with one complete cycle ABCDA.

Calculate the frequency of the oscillations.

Show that the amplitude of the oscillations is $3.4\text{ cm}$.

Calculate the maximum acceleration $a_0$ of the sphere.

On Fig. 4.2, sketch the variation with $x$ of the acceleration $a$ of the sphere.

Describe, without calculation, the interchange between the potential energy and the kinetic energy of the oscillations.

State, in terms of $V$ and $C$, expressions for: the initial charge $Q_{\text{A}}$ on the plates of capacitor A

State, in terms of $V$ and $C$, expressions for: the initial energy $E_{\text{A}}$ stored in capacitor A.

The two-way switch S is now moved to position Y. State and explain what happens to the charge that was initially on the plates of capacitor A.

Show that the final potential difference (p.d.) $V_{\text{B}}$ across capacitor B is given by $$V_{\text{B}}=\frac{V}{4}\mathrm{.}$$ Explain your reasoning.

Determine an expression, in terms of $V$ and $C$, for the decrease $\mathrm{\Delta }E$ in the total energy that is stored in the capacitors as a result of the change of the position of the switch.

Define magnetic flux.

Calculate the magnetic flux through the disc. Give a unit with your answer.

The disc is rotating at a rate of 25 revolutions per second. Calculate the magnitude of the electromotive force (e.m.f.) induced between the axle and the rim of the disc.

The axle and the rim are connected into an external circuit that enables the energy of the rotation of the disc to be stored for future use. The direction of rotation is shown in Fig. 6.1. Use Lenz’s law of electromagnetic induction to determine whether the current in the disc is from the rim to the axle or from the axle to the rim. Explain your reasoning.

State the name of the type of rectification produced by a bridge rectifier.

Complete Fig. 7.1 by drawing the three missing diodes, correctly connected.

On Fig. 7.1, draw an arrow to indicate the direction of the current in resistor R.

$V_{\text{IN}}$ has amplitude $V_0$ and period $T$. Fig. 7.2 shows the variation with time $t$ of $V_{\text{IN}}$. On Fig. 7.3, sketch the variation of $V_{\text{OUT}}$ with $t$ between $t=0$ and $t=2.0T$.

The power dissipated in the resistor is $P$. On Fig. 7.4, sketch the variation of $P$ with $t$ between $t=0$ and $t=2.0T$.

Suggest, with a reason, how the root-mean-square (r.m.s.) value of $V_{\text{OUT}}$ compares with the r.m.s. value of $V_{\text{IN}}$.

Explain, with reference to photons, why there is a single frequency of electromagnetic radiation that corresponds to each of these transitions.

On Fig. 8.2, draw a line that corresponds to the transition of the electron from $n=2$ to $n=1$. Label this line A.

On Fig. 8.2, draw a line that corresponds to the transition of the electron from $n=3$ to $n=2$. Label this line B.

The frequency of radiation represented by line A is $f_{\text{A}}$. The frequency of radiation represented by line B is $f_{\text{B}}$. The energy of the ground state ($n=1$) is $E_1$. Determine an expression, in terms of $f_{\text{A}}$, $f_{\text{B}}$, $E_1$ and the Planck constant $h$, for the energy $E_3$ of the energy level $n=3$.

Define mass defect.

Table 9.1 shows the mass defects of three nuclei. Table 9.1

The nuclear fusion process in a particular star is described by $${}_1^2\text{H}+{}_1^3\text{H}\to {}_2^4\text{He}+\text{X}$$ where X is a particle that has no mass defect. State the name of particle X.

Show that the energy released when one nucleus of ${}_2^4\text{He}$ is formed in this fusion reaction is $2.8\times {10}^{-12}\text{ J}$.

The star in (b) has a radius of $2.3\times {10}^9\text{ m}$ and a luminosity of $1.4\times {10}^{28}\text{ W}$. All the energy released from the formation of ${}_2^4\text{He}$ is radiated away from the star. All the energy that is radiated from the star has been released in the formation of ${}_2^4\text{He}$. Determine: the mass of ${}_2^4\text{He}$ produced per unit time by the fusion process

Determine: the surface temperature of the star.

State the name of the charged particles that are accelerated by the applied p.d.

Explain how X-rays are produced at the metal target.

Calculate the minimum wavelength of X-rays produced when the applied p.d. is $5.80\text{ kV}$.

X-rays pass through a medium that has an attenuation coefficient of $1.4{\text{ cm}}^{-1}$. Calculate the percentage of the X-ray energy that is absorbed by a $2.8\text{ cm}$ thickness of this medium.