科目：物理 Physics (9702)
年份：2025 冬季
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, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics, 25: Astronomy and cosmology
*0000800000004*
DFD
4
1 The Earth may be considered as a uniform sphere of radius $6.37 \times 10^6$ m.
Cambridge is at a point on the Earth’s surface that has a latitude of $52.2^\circ$ north of the Equator, as shown in Fig. 1.1.
<div style="text-align: center;">
</div>
Fig. 1.1
As the Earth spins on its axis, Cambridge moves in a circle that is parallel to the Equator but with a smaller radius.
(a) (i) Show that the radius of the circle around which Cambridge moves is $3.90 \times 10^6$ m.
[1]
(ii) Calculate the speed at which Cambridge moves around the circle.
speed = _________________________ m s⁻¹ [3]
© UCLES 2025
9702/42/O/N/25
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*0000800000005* DFD 5 (b) A student of mass 58.6 kg stands on horizontal ground in Cambridge. (i) Determine the magnitude of the resultant force that acts to cause the circular motion of the student. resultant force = ………………………………………… N [2] (ii) On Fig. 1.2, draw an arrow to show the direction of the resultant force that acts on the student. <!-- Image: Fig. 1.2 (not to scale) --> Fig. 1.2 (not to scale) [1] (iii) On Fig. 1.3, draw labelled arrows from the student to show the directions of the forces that act on the student to cause the resultant force in (b)(ii). <!-- Image: Fig. 1.3 (not to scale) --> Fig. 1.3 (not to scale) 2 © UCLES 2025 9702/42/O/N/25 [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
*0000800000006* DFD 6 2 (a) State Newton’s law of gravitation. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) One of the basic assumptions of the kinetic theory of gases is that there are no forces exerted between the molecules of the gas except during collisions. State two other basic assumptions of the kinetic theory of gases. 1 .................................................................................................................
*0000800000007* DFD 7 (d) (i) Use your answer in (c)(ii) to calculate the average gravitational force between adjacent molecules in hydrogen gas. average force = ………………………………………… N [2] (ii) By considering the weight of a molecule, suggest with a reason whether your answer in (d)(i) is consistent with the assumption of the kinetic theory of gases that there are no forces exerted between molecules. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 1 © UCLES 2025 9702/42/O/N/25 [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
*0000800000008* DFD 8 3 (a) State what is meant by two objects being in thermal equilibrium. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Fig. 3.1 shows a type of thermometer called a constant volume gas thermometer.  Fig. 3.1 (not to scale) The thermometer is used to determine the thermodynamic temperature $T$ of the gas in the glass bulb. The glass bulb is immersed in the environment for which the temperature is to
*0000800000009* DFD 9 (i) The value of $\Delta h$ can be used to calculate the pressure of the gas. In order to do this, the gravitational field strength is used, along with a property of the liquid. State the property of the liquid that is used to calculate the pressure. ........................................................................................................................... [1] (ii) Before the measurement of $\Delta h$ can be made, the glass bulb needs to reach thermal equilibrium with the environment for which the temperature is to be measured. State two disadvantages of using a constant volume gas thermometer to measure temperature. 1 ........................................................................................................................... 2
*0000800000010* DFD 10 4 A cylinder contains a fixed mass of an ideal gas at pressure $2Y$ and volume $6X$. The gas undergoes a sequence of changes from its initial state A, through states B, C and D, then finally back to its initial state A, as shown in Fig. 4.1.  Fig. 4.1 Fig. 4.2 shows the variation with time of the internal energy of the gas.  Fig. 4.2 (a) State the first law of thermodynamics. ............................................................................................................................... ............................................................................................................................... .......................................................................................
*0000800000011*
DFD
11
(b) (i) Use Fig. 4.1 and Fig. 4.2 to determine the general expression for the internal energy $U$ of the gas when it has pressure $p$ and volume $V$.
$$
U = \text{..................................................} [1]
$$
(ii) An ideal gas at thermodynamic temperature $T$ contains $N$ molecules.
Use your answer in (b)(i) and the equation of state for an ideal gas to deduce an expression for $U$ in terms of $N$ and $T$. Identify any other symbols you use.
$$
U = \text{..................................................} [2]
$$
(c) Determine expressions, in terms of $X$ and $Y$, for the work $W$ done on the gas during:
(i) change AB
$$
W = \text{..................................................} [1]
$$
(ii) change CD.
$$
W = \text{..........................*0000800000012* DFD 12 5 A steel ball on the end of a thin string oscillates with small oscillations, as shown in Fig. 5.1. <!-- Image: Fig. 5.1 (not to scale) --> Fig. 5.1 (not to scale) The displacement of the centre of the ball from its equilibrium position is $x$ . (a) Fig. 5.2 shows the variation with $x$ of the acceleration $a$ of the ball. <!-- Image: Fig. 5.2 --> Fig. 5.2 (i) Explain how Fig. 5.2 shows that the oscillations of the ball are simple harmonic. ............................................................................................................................... ............................................................................................................................... ..............................................................
*0000800000013*
DFD
13
(ii) Determine the period $T$ of the oscillations.
$$
T = \underline{\hspace{5cm}} \text{ s [3]}
$$
(b) At time $t = 0$ , when the displacement of the ball has its maximum value, the ball is immersed in a trough containing thick oil so that the ball is just below the surface of the oil. This results in the subsequent motion of the ball being heavily damped.
(i) State what is meant by damping.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ [2]
(ii) On Fig. 5.3, sketch a possible variation of the displacement $x$ of the ball with $t$ between $t = 0$ and $t = 2T$ .
Fig. 5.3
3
© UCLES 2025
9702/42/O/N/25
[Turn over]
Note: The image contains a graph labeled "Fig. 5.3" with axes labeled $x/\text{cm*0000800000014* DFD 14 6 (a) Define electric field at a point. ............................................................................................................................... ............................................................................................................................... [1] (b) An isolated conducting sphere in a vacuum has a capacitance of 69 pF. The charge on the sphere is +83 pC. (i) On Fig. 6.1, draw field lines to represent the electric field outside the sphere due to the charge on the sphere. Fig. 6.1 [2] (ii) Calculate the electric potential at the surface of the sphere. electric potential = ................................................... V [2] (iii) Determine the radius of the sphere. radius = .......................
*0000800000015*
DFD
15
(iv) Calculate the electric field strength $E$ at the surface of the sphere. Give a unit with your answer.
$$
E = \underline{\hspace{3cm}} \text{ unit} \quad [2]
$$
(c) The sphere in (b) is discharged by connecting it to earth (0 V) through a resistor of resistance 120 MΩ.
Calculate the time taken for the charge to fall to 26 pC.
$$
\text{time} = \underline{\hspace{3cm}} \text{ s} \quad [2]
$$
[Total: 11]
© UCLES 2025
9702/42/O/N/25
[Turn over]
---
**DO NOT WRITE IN THIS MARGIN**
**DO NOT WRITE IN THIS MARGIN**
**DO NOT WRITE IN THIS MARGIN**
**DO NOT WRITE IN THIS MARGIN**
**DO NOT WRITE IN THIS MARGIN**
**DO NOT WRITE IN THIS MARGIN**
**DO NOT WRITE IN THIS MARGIN**
**DO NOT WRITE IN THIS MARGIN**
---
*0000800000015*
DFD
15
(iv) Calculate t*0000800000016* DFD 16 7 An alternating voltage $V$ varies with time $t$ according to $$ V = 18 \cos 40\pi t $$ where $V$ is in V and $t$ is in s. (a) For the alternating voltage: (i) show that the period is 0.050 s [1] (ii) determine the root-mean-square (r.m.s.) voltage. r.m.s. voltage = ………………………………………… V [1] (b) On Fig. 7.1, sketch the variation of $V$ with $t$ for values of $t$ from $t = 0$ to $t = 100$ ms.  Fig. 7.1 [3] (c) The alternating voltage is rectified to produce an output voltage across a load resistor R, as shown in Fig. 7.2.  Fig. 7.2 © UCLES 2025 9702/42/O/N/25 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
*0000800000017* DFD 17 Fig. 7.3 shows the variation with $t$ of the power $P$ in the load resistor.  Fig. 7.3 State **three** conclusions that can be drawn from Fig. 7.3. The conclusions may be qualitative or quantitative. Use the space for any working. 1. ....................................................................................................................... .................................................................................................................... 2. ....................................................................................................................... .................................................................................................................... 3. ...............................
*0000800000018*
DFD
18
8 Fig. 8.1 shows the three lowest-frequency lines in the part of the emission spectrum for hydrogen that relates to electron transitions to the ground state (level $n = 1$).
<table>
<tr>
<td></td>
<td>3.09</td>
<td>2.92</td>
<td>2.47</td>
</tr>
</table>
Fig. 8.1 (not to scale)
The numbers represent the frequencies, in $10^{15}$ Hz, associated with the spectral lines.
(a) Use the photon model of electromagnetic radiation to explain how the existence of spectral lines in the emission spectrum provides evidence for discrete electron energy levels in the hydrogen atom.
...............................................................................................................................
................................................*0000800000019*
DFD
19
(iii) Complete Table 8.1 to show the energy differences from the ground state, and the energies of the levels up to $n = 4$, in the hydrogen atom. Use the space for any working.
---
**Table 8.1**
<table>
<thead>
<tr>
<th>level</th>
<th>(energy difference from $n = 1$)/eV</th>
<th>energy/eV</th>
</tr>
</thead>
<tbody>
<tr>
<td>$n = 4$</td>
<td></td>
<td></td>
</tr>
<tr>
<td>$n = 3$</td>
<td></td>
<td></td>
</tr>
<tr>
<td>$n = 2$</td>
<td>10.2</td>
<td></td>
</tr>
<tr>
<td>$n = 1$</td>
<td>0.0</td>
<td>−13.6</td>
</tr>
</tbody>
</table>
4
---
© UCLES 2025
9702/42/O/N/25
[Turn over]
<!-- Image: DO NOT WRITE IN THIS MARGIN *0000800000020*
DFD
20
9 (a) State what is meant by the mass defect of a nucleus.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) The nuclear fusion reaction for the formation of helium-4 from deuterium is represented by
$$
{}_{1}^{2}\text{H} + {}_{1}^{2}\text{H} \rightarrow {}_{2}^{4}\text{He}.
$$
Table 9.1 shows the masses of the nuclides involved in this reaction.
**Table 9.1**
<table>
<tr>
<th>nuclide</th>
<th>nuclide mass/u</t*0000800000021*
DFD
21
(c) The star Sirius has a radius of $1.19 \times 10^9$ m and loses mass due to nuclear fusion at a rate of $1.09 \times 10^{11}$ kg s $^{-1}$ . Assume that the power of the radiation emitted by the star is equal to the power released by this process.
(i) Determine a value for the luminosity of Sirius. Give a unit with your answer.
luminosity = ……………………………… unit ………… [2]
(ii) Use your answer in (c)(i) to determine the surface temperature of Sirius.
surface temperature = ………………………………… K [2]
(d) Explain how cosmologists use standard candles to estimate the distance of a galaxy from the Earth.
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
………*0000800000022*
DFD
22
10 (a) State what is meant by contrast in an X-ray image.
...............................................................................................................................
............................................................................................................................... [1]
(b) X-rays of intensity $I_0$ are incident normally on a structure, as shown in Fig. 10.1.
Fig. 10.1
Material P has a linear attenuation coefficient of $0.35 \text{cm}^{-1}$ .
The X-rays emerging from the structure in region A have an intensity of $0.053I_0$ .
(i) Show that the intensity of the X-rays emerging in region B is $0.13I_0$ .
[1]
© UCLES 2025
9702/42/O/N/25
DO NOT WRITE IN THIS MARGIN
DO NOT WRITE IN THIS M*0000800000023*
DFD
23
(ii) Determine the linear attenuation coefficient $\mu$ of material Q.
$\mu = \underline{\hspace{5cm}} \text{ cm}^{-1}$ [3]
(iii) Use the information in (b)(i) to suggest why the X-rays emerging from the structure form an image that has poor contrast.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{5cm}}$ [1]
(c) Explain how X-rays are used in computed tomography (CT) scanning to produce a three-dimensional image of an internal structure.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{5cm}}$ [3]
[Total: 9]
© UCLES 2025
9702/42/O/N/25
Note: The vertical text "DO NOT WRITE IN THIS MARGIN" on the left margin is not included in the Markdown as it is a formatting instruct