科目：物理 Physics (9702)
年份：2025 冬季
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, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics, 25: Astronomy and cosmology
*0000800000004* DFD 4 1 (a) In terms of velocity and acceleration, describe uniform circular motion of an object. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Fig. 1.1 shows the view from above of a polystyrene ball undergoing horizontal circular motion of radius $R$ . <!-- Image description: A diagram showing a screen with a point P on it, a dashed circle representing the path of a polystyrene ball centered at O, and a point B on the circle
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(i) State an expression, in terms of $R$ and $\omega$ , for the speed $v$ of the ball.
$v = \text{................................................... [1]}$
(ii) Determine an expression, in terms of $v$ and $\omega$ , for the centripetal acceleration of the ball.
centripetal acceleration = $\text{................................................... [2]}$
(c) The ball in (b) is in the position shown in Fig. 1.1, such that line OB is at an angle $\theta$ to the line OP.
(i) Determine an expression, in terms of $R$ and $\theta$ , for the displacement $x$ of the shadow from P.
$x = \text{................................................... [1]}$
(ii) The value of $\theta$ is zero at time $t = 0$ .
State an expression for $\theta$ in terms of $\omega$ and $t$ .
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(d) The circular motion of the ball in Fig. 1.1 has a diameter of $0.46\,\text{m}$ and an angular speed of $1.9\,\text{rad}\,\text{s}^{-1}$ .
For the simple harmonic motion of the shadow of the ball in Fig. 1.1, calculate:
(i) the amplitude
amplitude = ………………………………………… m [1]
(ii) the period
period = ………………………………………… s [2]
(iii) the maximum acceleration.
maximum acceleration = ………………………………………… $\text{m}\,\text{s}^{-2}$ [2]
(e) On Fig. 1.1, draw, and label with the letter A, the position of the shadow on the screen when the shadow has its maximum positive acceleration.
[Total: 15]
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DO NOT WRITE IN THIS MARGIN*0000800000007* DFD 7 --- 2 (a) State two ways in which the first law of thermodynamics describes that the internal energy of a system may be changed. 1 ............................................................................................................................... ............................................................................................................................ 2 ............................................................................................................................... ............................................................................................................................ [2] (b) (i) Use the first law of thermodynamics to explain why a bicycle pump gets hot when it is used to pump up a tyre quickly.
*0000800000008* DFD 8 3 (a) Define gravitational field at a point. ............................................................................................................................... ............................................................................................................................... [1] (b) Fig. 3.1 shows an isolated point mass of mass $M$ . mass $M$ $\bullet$ $\quad$ x $\quad$ $\bullet$ P Fig. 3.1 Point P is at distance $x$ from the point mass. (i) By considering the force exerted by the point mass on a test mass of mass $m$ placed at P, derive an equation for the gravitational field strength $g$ at P, in terms of $M$ and $x$ . Identify any other symbols you use. [2] (ii) On Fig. 3.1, draw an arrow to indicate the direction of the gravit
*0000800000009* DFD 9 (c) Two identical isolated uniform spheres X and Y each have radius $R$ . The centres of the spheres are separated by distance $L$ , as shown in Fig. 3.3. <div style="text-align: center;">  </div> Fig. 3.3 Point P lies on the line joining the centres of X and Y, and is at a variable displacement $x$ from the centre of sphere X. The gravitational field strength at the surface of each sphere is $g_0$ . On Fig. 3.4, sketch the variation with $x$ of the gravitational field $g$ at point P between $x = R$ and $x = L - R$ . <div style="text-align: center;">  </div> Fig. 3.4 3 © UCLES 2025 9702/41/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 I
*0000800000010* DFD 10 4 (a) State the value of absolute zero on: (i) the Celsius temperature scale temperature = …………………………………………°C [1] (ii) the thermodynamic temperature scale. Give a unit with your answer. temperature = ………………………………………… unit ……… [1] (b) A sample contains a fixed amount of gas. The gas has pressure $p$, volume $V$ and thermodynamic temperature $T$. Fig. 4.1 shows the variation of $pV$ with $kT$ for the sample, where $k$ is the Boltzmann constant.  Fig. 4.1 (i) State what is indicated about the nature of the gas from the variation shown in Fig. 4.1. ……………………………………………………………………………………………………… [1] (ii) Determine the number $N$ of molecules of the gas in the sample. $N =$ ……………………………………………………………… [2] © UCLES 2025 9702/41/O/N/25 DO NOT WRIT
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(iii) Use your answer in (b)(ii) to determine the amount $n$ of gas in the sample.
$n = \underline{\hspace{5cm}} \text{ mol [1]}$
(c) The root-mean-square (r.m.s.) speed of the molecules of the gas is $1900 \, \text{m} \, \text{s}^{-1}$ when $\rho V$ is equal to $270 \, \text{J}$ .
Determine the mass, in $u$ , of one molecule of the gas, where $u$ is the unified atomic mass unit.
$\text{mass} = \underline{\hspace{5cm}} u \, [4]$
[Total: 10]
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(iv) On Fig. 5.2, sketch the variation of $V$ with $x$ between $x = 10\,\text{pm}$ and $x = 110\,\text{pm}$ .
Fig. 5.2
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6 (a) Two parallel plate capacitors $C_1$ and $C_2$ are connected to a supply that has a potential difference (p.d.) $V_S$ . The capacitors may be connected in series or in parallel.
The supply provides charge $Q_S$ and the plates of the two capacitors acquire charges $Q_1$ and $Q_2$ respectively. The p.d.s across the plates of the capacitors are $V_1$ and $V_2$ respectively.
Complete Table 6.1 to indicate how $Q_S$ , $Q_1$ and $Q_2$ relate to each other, and how $V_S$ , $V_1$ and $V_2$ relate to each other, for series and parallel connections of the capacitors to the supply.
Table 6.1
<table>
<tr>
<th></th>
<th>relationship between charges</th>
<th>relationship between p.d.s</th>
</tr>
<tr>
<td>series</td>
<td></td>
<td></td>
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(iii) The capacitor is now connected in parallel with a capacitor of capacitance $180\,\mu\text{F}$ that is initially uncharged.
Determine the total energy, in mJ, now stored in the two capacitors.
energy = ………………………………………… mJ 3
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7 (a) State Faraday’s law of electromagnetic induction.
...............................................................................................................................
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............................................................................................................................... [2]
(b) An aircraft is flying horizontally at constant speed $v$ through the Earth’s magnetic field, as shown in Fig. 7.1.
<!-- Image: VIEW FROM SIDE and VIEW FROM ABOVE -->
VIEW FROM SIDE
VIEW FROM ABOVE
Fig. 7.1
At the location of the aircraft, the vertical component of the Earth’s magnetic field is $38\,\mu\text{T}$ towa*0000800000017* DFD 17 (ii) Determine the area of flux cut by the wings in a time of 15 s. area = ………………………………………… m² [2] (iii) Use your answer in (b)(ii) to determine the speed $v$ of the aircraft. $v$ = ………………………………………… m s⁻¹ [2] (iv) Use Lenz’s law of electromagnetic induction to explain which of the wingtips P and Q is at the higher induced potential. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 3 © UCLES 2025 9702/41/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
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8 (a) State what is meant by a photon.
...............................................................................................................................
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............................................................................................................................... [2]
(b) A stationary nucleus of uranium-238 ( $^{238}_{92}\text{U}$ ) undergoes alpha decay to produce a nucleus of thorium-234 ( $^{234}_{90}\text{Th}$ ). The kinetic energy of the emitted alpha particle is 4.200 MeV. A gamma-ray photon is also emitted during the decay.
Assume that the rebound kinetic energy of the thorium nucleus is negligibl*0000800000019*
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(ii) Determine a value for the wavelength of the gamma radiation emitted during the decay of the uranium-238 nucleus.
wavelength = ………………………………………… m [3]
(iii) In practice, the rebound kinetic energy of the thorium nucleus is **not** negligible.
Explain, without further calculation, how your answer in (b)(ii) compares with the true wavelength of gamma radiation emitted during the decay of the uranium-238 nucleus.
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
……………………………………………………………………………………………………… [1]
(c) Gamma radiation emitted during the decay of a sample of uranium-238 has a single wavelength.
Nuclei of cobalt-60 ( $^{60}_{27}\text{Co}$ ) decay by beta emission, and also emit gamma radiation in the process.
Suggest w*0000800000020*
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9 (a) State Wien’s displacement law.
...............................................................................................................................
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............................................................................................................................... [2]
(b) Fig. 9.1 shows the variation with $d^{-2}$ of the radiant flux intensity $F$ observed from a star X, where $d$ is the distance of the observer from the star. Fig. 9.2 shows the variation with wavelength $\lambda$ of the rates of emission $P$ of radiation by star X and the Sun.
<div style="display: flex; justify-content: space-between;">
*0000800000021* DFD 21 (c) Star X is in a galaxy that is moving away from the Earth. Suggest, with a reason, how the line for star X in Fig. 9.2 would appear differently if it had been obtained from data measured on the Earth. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... 2 © UCLES 2025 9702/41/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
*0000800000022* DFD 22 10 (a) Define specific acoustic impedance. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Explain how ultrasound waves are detected by a piezoelectric crystal. ............................................................................................................................... ............................................................................................................................... ......
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