科目：物理 Physics (9702)
年份：2023 夏季
试卷：Paper 41
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
4 1 (a) (i) Define gravitational field. ............................................................................................................................ [1] (ii) Define electric field. ............................................................................................................................ [1] (iii) State one similarity and one difference between the gravitational potential due to a point mass and the electric potential due to a point charge. similarity: ............................................................................................................................ difference: ............................................................................................................................ [2] (b) An isolated uniform conducting
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(c) Assume that the Earth is a uniform conducting sphere of mass $5.98 \times 10^{24} \, \text{kg}$ .
The surface of the Earth carries a charge of $-4.80 \times 10^5 \, \text{C}$ that is evenly distributed.
(i) Use the information in (b) to determine the electric field strength at the surface of the Earth. Give a unit with your answer.
electric field strength = …………………………… unit …………… [2]
(ii) State how the direction of the electric field at the surface of the Earth compares with the direction of the gravitational field.
……………………………………………………………………………………………………… 1
© UCLES 2023 9702/41/M/J/23 [Turn over6 2 A steel sphere of mass 0.29 kg is suspended in equilibrium from a vertical spring. The centre of the sphere is 8.5 cm from the top of the spring, as shown in Fig. 2.1. <div style="text-align: center;">  </div> Fig. 2.1 The sphere is now set in motion so that it is moving in a horizontal circle at constant speed, as shown in Fig. 2.2. <div style="text-align: center;">  </div> Fig. 2.2 The distance from the centre of the sphere to the top of the spring is now 10.8 cm. (a) Explain, with reference to the forces acting on the sphere, why the length of the spring in Fig. 2.2 is greater than in Fig. 2.1. ............................................................................................................................... .......
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(b) The angle between the linear axis of the spring and the vertical is $27^\circ$ .
(i) Show that the radius $r$ of the circle is 4.9 cm.
[1]
(ii) Show that the tension in the spring is 3.2 N.
[2]
(iii) The spring obeys Hooke’s law.
Calculate the spring constant, in N cm $^{-1}$ , of the spring.
spring constant = ……………………………… N cm $^{-1}$ [2]
(c) (i) Use the information in (b) to determine the centripetal acceleration of the sphere.
centripetal acceleration = ……………………………… m s $^{-2}$ [2]
(ii) Calculate the period of the circular motion of the sphere.
period = ……………………………… s 2
© UCLES 2023 9702/41/M/J/23 [Turn over8 3 (a) State the reason why two objects that are at the same temperature are described as being in thermal equilibrium. ............................................................................................................................ [1] (b) Fig. 3.1 shows the variations with temperature of the densities of mercury and of water between 0°C and 100°C. <div style="display: flex; justify-content: space-between; width: 100%;"> <div style="width: 45%;"> density ↑ mercury 0 temperature/°C 100 </div> <div style="width: 45%;"> density ↑ water 0 temperature/°C 100 </div> </div> Fig. 3.1 Temperature may be measured using the variation with temperature of the density of a liquid. Suggest why, for measuring temperature over this temperature range: (i) mercury is a
9 temperature/°C 100 75 50 25 0 0 10 20 30 40 50 60 t/s Fig. 3.2 (i) State the boiling temperature, in °C, of the liquid. temperature = ………………………………………… °C [1] (ii) Determine the specific heat capacity, in Jg⁻¹K⁻¹, of the liquid. specific heat capacity = ………………………………………… Jg⁻¹K⁻¹ [4] (d) The experiment in (c) is repeated using water instead of the liquid in (c). The mass of liquid used, the power supplied, and the initial temperature are all unchanged. The specific heat capacity of water is approximately twice that of the liquid in (c). The boiling temperature of water is 100°C. On Fig. 3.2, sketch the variation with time $t$ of the temperature of the water between $t = 0$ and $t = 60$ s. Numerical calculations are not required. 2 © UCLES 2023 9702/41/M/J/2
10 4 (a) State two of the basic assumptions of the kinetic theory of gases. 1 ............................................................................................................................... ............................................................................................................................... 2 ............................................................................................................................... ............................................................................................................................... [2] (b) An ideal gas has amount of substance $n$. The gas is initially in state X, with pressure $2p$ and volume $V$. The gas is cooled at constant volume to state Y, with pressure $p$. The gas is t
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(iii) During the change of state from Y to Z, the increase in internal energy of the gas is $U$. During the change of state from Z to X, the work done on the gas is $W$.
Complete Table 4.1 to indicate, for each of the three changes of state, the increase in internal energy of the gas, the thermal energy transferred to the gas and the work done on the gas, in terms of $p$, $V$, $U$ and $W$.
Table 4.1
<table>
<tr>
<th>change</th>
<th>increase in internal energy of gas</th>
<th>thermal energy transferred to gas</th>
<th>work done on gas</th>
</tr>
<tr>
<td>X to Y</td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>Y to Z</td>
<td>+U</td>
<td></td>
<td></td>
</tr>
<tr>
<td>Z to X</td>
<td></td>
<td></td>
<td>+W<12
5 Part of an electric circuit is shown in Fig. 5.1.
<div style="text-align: center;">
</div>
Fig. 5.1
The circuit is used to produce half-wave rectification of an alternating voltage of potential difference (p.d.) $V_{IN}$.
The output p.d. across the 14 kΩ resistor is $V_{OUT}$.
(a) (i) A component is missing from the circuit of Fig. 5.1.
Complete the circuit diagram in Fig. 5.1 by adding the circuit symbol for the missing component, correctly connected. [1]
(ii) A capacitor C is shown in the circuit of Fig. 5.1.
State the effect on $V_{OUT}$ of including the capacitor in the circuit. [1]
(b) Fig. 5.2 shows the variation with time $t$ of $V_{IN}$.
<div style="text-align: center;">
</div>
Fig. 5.2
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Fig. 5.3 shows the variation with $t$ of $V_{OUT}$
Fig. 5.3
(i) Determine the frequency of $V_{IN}$
frequency = ………………………………………… Hz [1]
(ii) Show that the time constant $\tau$ for the discharge of the capacitor through the resistor is 0.038 s.
[2]
(iii) Calculate the capacitance of C. Give a unit with your answer.
capacitance = ………………………………………… unit …………… [2]
(c) The circuit of Fig. 5.1 is modified so that it produces full-wave rectification of an input voltage. Suggest, with a reason, how $V_{OUT}$ now varies with time when $V_{IN}$ is as shown in Fig. 5.2.
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
……………………………………………………………………………………………………… 2
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6 (a) State what is meant by a magnetic field.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) A long, straight wire P carries a current into the page, as shown in Fig. 6.1.
$\otimes$ $\xrightarrow{\text{wire P current into page}}$
Fig. 6.1
On Fig. 6.1, draw four field lines to represent the magnetic field around wire P due to the current in the wire. [3]
(c) A second long, straight wire Q, carrying a current of 5.0A out of the page, is pla15 (ii) State the direction of the force exerted on wire Q by wire P. ................................................................................................................... [1] (iii) The flux density of the magnetic field at wire P due to the current in wire Q is 1.5 mT. Determine the magnitude of the current in wire P. Explain your reasoning. current = ................................................... A 2 © UCLES 2023 9702/41/M/J/23 [Turn over
16 7 (a) State what is meant by the de Broglie wavelength. ............................................................................................................................ [1] (b) Fig. 7.1 shows a glass tube in which electrons are accelerated through a high p.d. to form a beam that is incident on a thin graphite crystal.  Fig. 7.1 (not to scale) After passing through the graphite crystal, the electrons reach the fluorescent screen. The screen glows where the electrons strike it. Fig. 7.2 shows the fluorescent screen viewed end-on, from the right-hand side of Fig. 7.1.  Fig. 7.2 © UCLES 2023 9702/41/M/J/23
17 (i) State the name of the phenomenon demonstrated by the pattern shown in Fig. 7.2. ................................................................................................................... [1] (ii) Explain what can be concluded from the pattern in Fig. 7.2 about the nature of electrons. ................................................................................................................... ................................................................................................................... ................................................................................................................... [2] (c) The electrons in (b) are now accelerated through a greater potential difference between the cathode and the anode. (i) On Fig. 7.3
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8 (a) Table 8.1 shows some data relating to the properties of air, gel and body tissue. The data are given to three significant figures.
Table 8.1
<table>
<tr>
<th>material</th>
<th>density/kg m⁻³</th>
<th>speed of sound/m s⁻¹</th>
<th>specific acoustic impedance/kg m⁻² s⁻¹</th>
</tr>
<tr>
<td>air</td>
<td></td>
<td>340</td>
<td>440</td>
</tr>
<tr>
<td>gel</td>
<td>1200</td>
<td>1400</td>
<td></td>
</tr>
<tr>
<td>tissue</td>
<td>1090</td>
<td></td>
<td>1.68 × 10⁶</td>
</tr>
</table>
(i) Show that the specific acoustic impedance of gel is $1.68 \times 10^6 \, \text{kg} \, \text{m}^{-2} \, \text{s}^{-1}$ .
[1]
(ii) Complete Table 8.1 by calculating the missing values to three significant figures. Use the19 (c) Use your answers in (b) to explain why gel is applied to the skin during ultrasound scanning. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... 2 © UCLES 2023 9702/41/M/J/23 [Turn over
20 9 Carbon-11 is radioactive and decays by $\beta^+$ emission to form boron-11. Carbon-11 has a half-life of 20 minutes. Boron-11 is stable. (a) Define half-life. ............................................................................................................................... ............................................................................................................................... [1] (b) A sample contains $N_0$ nuclei of carbon-11 and no other nuclei at time $t = 0$ . On Fig. 9.1, sketch the variation with $t$ of the number of nuclei of boron-11 in the sample.  Fig. 9.1 [3] (c) (i) Explain, with reference to the random nature of radioactive decay, why the activity of the carbon-11 sample in (b) decreases with time. .....
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10 (a) State Hubble’s law. Identify any symbols that you use.
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) A star of luminosity $3.8 \times 10^{31} \, \text{W}$ is a distance of $1.8 \times 10^{24} \, \text{m}$ from the Earth.
Calculate the radiant flux intensity at the Earth of the radiation emitted by the star.
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