科目：物理 Physics (9702)
年份：2024 夏季
试卷：Paper 42
总页数：20
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 18: Electric fields, 19: Capacitance, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics, 25: Astronomy and cosmology
*0019655342204* 4 1 (a) Define the radian. ............................................................................................................................ [1] (b) A circular metal disc spins horizontally about a vertical axis, as shown in Fig. 1.1. <!-- Image: Fig. 1.1 (not to scale) --> Fig. 1.1 (not to scale) 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: (i) an arrow, labelled V, showing the direction of the velocity of the modelling clay [1] (ii) an arrow, labelled A, showing the direction of the acceleration of the modelling clay. [1] (c) The metal disc in Fig. 1.1 has a radius of 9.3 cm. The centre of gravity of the modelling clay is 1.2 cm from the rim of the dis
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(ii) Calculate the acceleration $a$ of the centre of gravity of the modelling clay.
$a = \underline{\hspace{5cm}} \text{ m s}^{-2} \text{ [2]}$
(d) A second piece of modelling clay is attached to the disc in the position shown in Fig. 1.2.
Fig. 1.2
The second piece of modelling clay has a larger mass than the first piece.
By placing one tick ( $\checkmark$ ) in each row, complete Table 1.1 to show how the quantities indicated compare for the two pieces of modelling clay.
Table 1.1
<table>
<tr>
<th>quantity</th>
<th>less for second piece than first piece</th>
<th>same for both pieces</th>
<th>greater for second piece than first piece</th>
</tr>
<tr>
<td>angular speed</td>
<td></td>
<td></td>
<td></td>
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2 (a) With reference to thermal energy, state what is meant by two objects being in thermal equilibrium.
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(b) 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 \*0019655342207* 7 (iii) 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. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... 3 © UCLES 2024
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*0019655342209* 9 3 (a) State what is meant by the internal energy of a system. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) With reference to molecular kinetic and potential energies, describe and explain how the internal energy of the system changes when: (i) a gas is heated at constant volume so that its temperature increases ..................................................................................................................
*0019655342210* 10 4 A block of mass $m$ oscillates vertically on a spring, as shown in Fig. 4.1.  Fig. 4.1 The acceleration $a$ of the block varies with displacement $x$ from its equilibrium position, as shown in Fig. 4.2.  Fig. 4.2 The amplitude of the oscillations is $3Y$ and the maximum acceleration is $2A$. (a) Explain how Fig. 4.2 shows that the oscillations of the block are simple harmonic. ............................................................................................................................... ............................................................................................................................... .........................................................................................
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(b) Deduce expressions, in terms of some or all of $m$ , $A$ and $Y$ , for:
(i) the angular frequency $\omega$ of the oscillations
$\omega = \underline{\hspace{5cm}}$ [1]
(ii) the maximum speed $v_0$ of the oscillations
$v_0 = \underline{\hspace{5cm}}$ [2]
(iii) the energy $E$ of the oscillations.
$E = \underline{\hspace{5cm}}$ [2]
(c) The period of the oscillations is 0.75 s and the value of $3Y$ is 1.8 cm.
Determine an expression for $x$ in terms of time $t$ , where $x$ is in cm and $t$ is in seconds.
$x = \underline{\hspace{5cm}}$ 2
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DO NOT WRI*0019655342212* 12 5 (a) Define electric potential at a point. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Two isolated charged metal spheres X and Y are near to each other in a vacuum. The centres of the spheres are 1.2 m apart, as shown in Fig. 5.1. <div style="text-align: center;">  </div> Fig. 5.1 (not to scale) Point P is on the line joining the centres of spheres X and Y and is at a variable distance x from the
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State three conclusions that may be drawn about the spheres from Fig. 5.2. The conclusions may be qualitative or quantitative.
1. ...............................................................................................................................
2. ...............................................................................................................................
3. ...............................................................................................................................
[3]
(c) 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.
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6 (a) Two capacitors X and Y are connected in series to a power supply of voltage $V$ , as shown in Fig. 6.1.
<div style="text-align: center;">
<br/>
Fig. 6.1
</div>
The capacitance of X is $C_x$ and the capacitance of Y is $C_y$ .
Derive an expression, in terms of $C_x$ and $C_y$ , for the combined capacitance $C_T$ of the capacitors in this circuit.
Explain your reasoning.
[3]
(b) 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 $C_Q$ of Q can be varied between 0 and $400\,\mu\text{F}$ .
When $C_Q = 0$ , the total energy stored in the capacitors is $2.5\,\text{mJ}$ .
(i) Show that the supply voltage $V$ is $5.0\,\text{V}$ .
[2]
© UCLE*0019655342315* 15 (ii) Calculate the total energy, in mJ, stored in the capacitors when $C_Q$ has its maximum value. total energy = ………………………………………… mJ [3] (iii) On Fig. 6.2, sketch the variation of the total energy $E$ stored in the capacitors with $C_Q$ , as $C_Q$ varies from 0 to 400 $\mu$ F.  Fig. 6.2 2 © UCLES 2024 9702/42/M/J/24 [Turn over] DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE
*0019655342316* 16 7 (a) State Faraday’s law of electromagnetic induction. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Fig. 7.1 shows a coil at rest in a uniform magnetic field that is parallel to the axis of the coil.  Fig. 7.1 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.  Fig. 7.2 The coil consi
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(ii) Determine the maximum rate of change of magnetic flux linkage in the coil.
maximum rate of change of flux linkage = ………………………………………… Wb s⁻¹ [3]
(iii) State the maximum electromotive force (e.m.f.) $V_0$ induced across the coil.
$$
V_0 = \text{……………………………………… V [1]}
$$
(iv) On Fig. 7.3, sketch the variation of the e.m.f. $V$ induced across the coil with $t$ from $t = 0$ to $t = 6.0$ ms.
Fig. 7.3
[3]
(v) 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.
$$
A = \text{……………………………………… unit ………………}
$$
$$
B = \text{……………………………………… unit ………………}
$$
3
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8 Fig. 8.1 shows part of the emission spectrum of visible radiation emitted by hydrogen gas in a star in a distant galaxy.
increasing frequency →
<table>
<tr>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
</table>
Fig. 8.1
The galaxy is moving away from the Earth at a speed of $6.2 \times 10^6 \, \text{m} \, \text{s}^{-1}$ .
(a) (i) 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.
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(iii) Determine the wavelength, in nm, of this radiation as detected by the observer on the Earth.
wavelength = ……………………………………… nm [2]
(c) A value for the Hubble constant is $2.3 \times 10^{-18} \, \text{s}^{-1}$ .
Determine the distance of the galaxy from the Earth.
distance = ……………………………………… m 2
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9 (a) State what is meant by the binding energy of a nucleus.
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(b) Table 9.1 shows the masses of two sub-atomic particles and a polonium-212 ( $^{212}_{84}\text{Po}$ ) nucleus.
Table 9.1
<table>
<tr>
<th></th>
<th>mass/u</th>
</tr>
<tr>
<td>proton</td>
<td>1.007276</td>
</tr>
<tr>
<td>neutron</td>
<td>1.008665</td>
</tr>
<tr>
<td>polonium-212*0019655342321* 21 (c) (i) On Fig. 9.1, sketch the variation with nucleon number $A$ of binding energy per nucleon for values of $A$ from 1 to 250. binding energy per nucleon $\uparrow$ 0 ———————————————————————————————— 1 ———————————————————————————————— 250 A Fig. 9.1 [2] (ii) On your line in Fig. 9.1, draw an X to show the approximate position of polonium-212. [1] (iii) 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. ............................................................................................................................... ..............................................................................................................
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*0019655342323* 23 10 (a) Describe how reflected ultrasound pulses may be used to obtain diagnostic information about internal structures. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) (i) Define specific acoustic impedance of a medium. .................................................................................