科目：物理 Physics (9702)
年份：2025 春季
试卷：Paper 42
总页数：24
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 18: Electric fields, 19: Capacitance, 20: Magnetic fields, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics, 25: Astronomy and cosmology
*0000800000004* 4 1 A steel ball is placed on the inside surface of a hollow circular cone. The ball moves in a horizontal circle at constant speed, as shown in Fig. 1.1. <!-- Image: Fig. 1.1 --> Fig. 1.1 The angle of the side of the cone to the horizontal is $52^\circ$ . There is no friction between the ball and the cone. (a) Fig. 1.2 shows a cross-section through the cone and the steel ball. <!-- Image: Fig. 1.2 --> Fig. 1.2 On Fig. 1.2, draw labelled arrows to show the two forces acting on the ball. [1] (b) Describe how the forces acting on the ball cause its acceleration to be centripetal. ............................................................................................................................... ...........................................................
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(c) The ball moves in a circle of radius 0.15m.
Show that the speed of the ball is $1.4 \, \text{m} \, \text{s}^{-1}$ .
[3]
(d) Calculate the angular speed $\omega$ of the ball.
$\omega = \underline{\hspace{5cm}} \, \text{rad} \, \text{s}^{-1}$ [2]
(e) The speed of the ball is increased.
Explain why the radius of the circular path of the ball increases.
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2 (a) The magnitude of the gravitational potential on the surface of a planet of radius $R$ is $\phi$ . The planet can be considered to be an isolated sphere.
On Fig. 2.1, sketch the variation of the gravitational potential with distance $x$ from the centre of the planet for values of $x$ between $R$ and $4R$ .
<div style="text-align: center;">
<br>
Fig. 2.1
</div>
[3]
(b) A satellite is in a geostationary orbit above the Earth. At time $t = 0$ , the magnitude of the gravitational potential due to the Earth at the location of the satellite is $\phi$ .
On Fig. 2.2, sketch the variation of the gravitational potential due to the Earth at the location of the satellite for values of $t$ between $t = 0$ and $t = 24$ hours.
<div style="t*0000800000007* 7 (c) The electric potential difference (p.d.) between two parallel plates is $V$, as shown in Fig. 2.3. <div style="text-align: center;">  </div> Fig. 2.3 The distance between the plates is $d$. The region between the plates is a vacuum. On Fig. 2.4, sketch the variation of the electric potential with distance from the positive plate. <div style="text-align: center;">  </div> Fig. 2.4 2 © UCLES 2025 9702/42/F/M/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 DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO N
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3 (a) Two metal cuboids P and Q are in thermal contact with each other.
(i) P and Q are in thermal equilibrium.
State what is meant by the term thermal equilibrium.
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(ii) Data for P and Q are given in Table 3.1.
Table 3.1
<table>
<tr>
<th></th>
<th>P</th>
<th>Q</th>
</tr>
<tr>
<td>specific heat capacity / J kg⁻¹ K⁻¹</td>
<td>390</td>
<td>910</td>
</tr*0000800000010*
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(b) Nitrogen may be assumed to be an ideal gas. A fixed amount of nitrogen gas is contained at a constant pressure of $1.6 \times 10^5 \, \text{Pa}$ .
The variation of the volume $V$ of the gas with the temperature $\theta$ of the gas is shown in Fig. 3.1.
Fig. 3.1
(i) The temperature of the nitrogen gas is increased from $0^\circ \text{C}$ to $210^\circ \text{C}$ . Determine the work done on the gas.
work done = ___________________________ J [3]
(ii) Determine the number $N$ of molecules of nitrogen gas.
$N = $ ___________________________ [2]
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(iii) The mass of a nitrogen molecule is $4.7 \times 10^{-26} \text{kg}$ .
Calculate the root-mean-square (r.m.s.) speed of a nitrogen molecule at $210^\circ \text{C}$ .
r.m.s. speed = _________________________ $\text{m s}^{-1}$ 2
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4 A small crystal is made to vibrate with simple harmonic motion. The variation with time $t$ of the displacement $x$ of one surface of the crystal from its equilibrium position is shown in Fig. 4.1.
Fig. 4.1
(a) Show that the angular frequency of the vibration of the surface is $4.2 \times 10^7 \, \text{rad} \, \text{s}^{-1}$ .
[2]
(b) Determine the maximum acceleration $a_0$ of the vibration of the surface.
$$
a_0 = \underline{\hspace{5cm}} \, \text{m} \, \text{s}^{-2} \, [2]
$$
(c) The crystal may be modelled as a single mass of $2.4 \times 10^{-4} \, \text{kg}$ that vibrates as shown in Fig. 4.1.
Calculate the total energy $E$ of the vibrations.
$$
E = \underline{\hspace{5cm}} \, \text{J} \, [3]
$$
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DO NO*0000800000013* 13 (d) The crystal generates ultrasound waves that are used to obtain diagnostic information about internal structures. (i) The crystal is made from piezoelectric material. Explain how the crystal is made to vibrate. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) A parallel beam of ultrasound waves i
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5 (a) A capacitor of capacitance $C_1$ is connected in series with a second capacitor of capacitance $C_2$ .
Show that the combined capacitance $C$ of the two capacitors is given by
$$
\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_2}.
$$
[2]
(b) Three identical capacitors, each of capacitance $C$ , are connected in a network as shown in Fig. 5.1.
<!-- Image: Fig. 5.1 -->
Fig. 5.1
The variation of the charge $Q$ with the potential difference (p.d.) $V$ between the terminals X and Y is shown in Fig. 5.2.
<!-- Image: Fig. 5.2 -->
Fig. 5.2
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Show that $C$ is equal to $44\,\mu\text{F}$ .
[3]
(c) The capacitor network in Fig. 5.1 is charged and then connected to a resistor of resistance $54\,\text{k}\Omega$ . The capacitor network discharges through the resistor.
(i) Determine the time constant $\tau$ of the circuit. Give a unit with your answer.
$\tau = \underline{\hspace{3cm}} \text{ unit} \hspace{1cm} [2]$
(ii) Determine the time taken for the discharge current to reduce to 15% of the initial discharge current.
$\text{time} = \underline{\hspace{6cm}} \text{ s} \hspace{1cm} [2]$
[Total: 9]
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6 An electric field and a magnetic field are used to form a velocity selector. Charged particles, called ions, pass into a region of uniform electric and magnetic fields that is between parallel plates, as shown in Fig. 6.1.
Fig. 6.1
(a) The potential difference (p.d.) between the plates of the velocity selector is $V$ . The separation of the plates is $d$ and the magnetic flux density is $B$ .
Show that the speed $u$ of ions that pass undeviated through the velocity selector is given by
$$
u = \frac{V}{Bd}.
$$
[2]
(b) Positive ions with kinetic energy $4.1 \times 10^{-17} \text{J}$ and mass $3.2 \times 10^{-27} \text{kg}$ pass undeviated through the velocity selector when $V$ is equal to $980 \text{V}$ and $d$ is equal to $3.6 \times 10^{-*0000800000017* 17 (c) A proton passes undeviated through the velocity selector. An alpha particle enters the velocity selector at the same speed as the proton. State how the expression in (a) predicts that the alpha particle also passes undeviated through the velocity selector. ............................................................................................................................ [1] (d) By reference to Fig. 6.1 and to the forces acting on a positive ion, determine the direction of the magnetic field. Explain your reasoning. ............................................................................................................................ [3] (e) The positive ions in (b) enter the velocity selector with greater kinetic energy. On Fig. 6.1, sketch the
*0000800000018* 18 7 (a) State Faraday’s law of electromagnetic induction. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A metal rod is accelerated uniformly from rest in a uniform magnetic field as shown in Fig. 7.1. rod × × × × — magnetic field
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(ii) Use Faraday’s law to show that the variation of $E$ with time $t$ is given by
$$
E = Blat
$$
where $a$ is the acceleration of the rod.
[3]
(iii) The length of the rod is $0.45\,\text{m}$ . The acceleration $a$ of the rod is $7.8\,\text{m}\,\text{s}^{-2}$ .
Determine the value of $B$ .
$$
B = \underline{\hspace{5cm}} \quad \text{T} \quad [2]
$$
[Total: 9]
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DO NOT WRITE IN TH* 0000800000020 * 20 BLANK PAGE © UCLES 2025 9702/42/F/M/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 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 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 WRI
*0000800000021* 21 8 (a) State what is meant by a photon. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A laser emits red light of a single wavelength. The light is produced when electrons move from a higher energy level to a lower energy level. The difference in energy between the two levels is 1.96 eV. (i) Calculate the wavelength of the light. wavelength = ................................................... m [3] (ii) The power of the bea
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9 Polonium-193 ( $^{193}_{84}\text{Po}$ ) is an unstable nuclide. A nucleus of polonium-193 decays to a nucleus of lead-189 ( $^{189}_{82}\text{Pb}$ ) by emitting an alpha-particle.
(a) Radioactive decay is both random and spontaneous.
State what is meant by:
(i) random
........................................................................................................................... [1]
(ii) spontaneous.
........................................................................................................................... [1]
(b) Define half-life.
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(c) Data for the binding energy per nucleon of the particles involved in th*0000800000023* 23 (d) A pure sample of polonium-193 contains $N_0$ nuclei. After a time $t$ the sample contains $N$ nuclei of polonium-193. The variation of $\ln(N/N_0)$ with $t$ is shown in Fig. 9.1.  Fig. 9.1 (i) State the name of the quantity that is represented by the magnitude of the gradient of the line in Fig. 9.1. ................................................................................................................... [1] (ii) Use Fig. 9.1 to determine the half-life, in ms, of polonium-193. half-life = ................................................... ms [2] © UCLES 2025 9702/42/F/M/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 MARG
*0000800000024* 24 (e) Positron emission tomography (PET scanning) uses a radioactive tracer. (i) State what happens to the positrons emitted by the tracer. ........................................................................................................................... [1] (ii) Explain why a tracer with a half-life of approximately 2 hours is a suitable tracer to use. ........................................................................................................................... 1 © UCLES 2025 9702/42/F/M/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 WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MA
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*0000800000026* 26 10 (a) (i) State what is meant by the luminosity of a star. ........................................................................................................................... [1] (ii) Explain how standard candles are used to determine the distance to a galaxy. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... [3] (b
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(i) The Sun rotates with a period of $2.07 \times 10^6$ s.
Show that the radius of the Sun is $6.93 \times 10^8$ m.
[3]
(ii) State and explain how the expected wavelength of the light observed from Z compares with the emitted wavelength.
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(iii) The luminosity of the Sun is $3.8 \times 10^{26}$ W.
Use the information in (b)(i) to calculate the surface temperature of the Sun.
temper