科目：物理 Physics (9702)
年份：2025 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
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1 (a) Define the radian.
............................................................................................................................ [1]
(b) The rear wheel and the pedals of a bicycle are connected by a chain that passes around two cogs (toothed wheels), as shown in Fig. 1.1.
Fig. 1.1 (not to scale)
The small cog has a radius of 0.038 m and is fixed to the rear wheel so that it rotates with it. The large cog has a radius of 0.15 m and is fixed to the pedals so that it rotates with them. The rear wheel has a radius of 0.46 m.
The bicycle is being pedalled so that it moves in a straight line at a constant speed of $17 \, \text{m} \, \text{s}^{-1}$ .
(i) Calculate the angular speed of the rear wheel.
angular speed = .....*0000800000005* DFD 5 (ii) Calculate the period of rotation of the small cog. period = ………………………………………… s [2] (iii) Show that the distance moved by point X on the chain during one full rotation of the small cog is 0.24 m. [1] (iv) Use the information in (b)(iii) to determine the angle through which the large cog rotates during one full rotation of the small cog. angle = ………………………………………… rad [2] (c) The chain of the bicycle in (b) is moved onto a smaller cog fixed to the rear wheel. The speed of the bicycle does not change. Explain, without calculation, the effect of this change on the angular speed of the pedals. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 2 © UCLES 2025 9702/42/M/J/25 [Turn over]
*0000800000006* DFD 6 2 (a) (i) State what is represented by a gravitational field line. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) The Earth may be considered as a uniform sphere, as shown in Fig. 2.1. <center> Earth </center> Fig. 2.1 On Fig. 2.1, draw field lines to represent the Earth’s gravitational field outside the Earth. [2] (b) The Earth’s magnetic field may be considered as being due to the Earth acting as a long solenoid,
*0000800000007* DFD 7 Fig. 2.3 is a copy of Fig. 2.2 without the labels but with two magnetic field lines shown. <!-- Image: A diagram showing a circular object with two magnetic poles, one labeled N and another S, with arrows indicating magnetic field lines extending from the poles. --> Fig. 2.3 (i) On Fig. 2.3, label the magnetic poles with the letters N and S to indicate which one is the magnetic N pole and which one is the magnetic S pole. [1] (ii) On Fig. 2.3, draw field lines to represent the Earth’s magnetic field outside the Earth. [2] (c) An observer moves around the surface of the Earth. (i) Use your answer in (a)(ii) to explain why the observed gravitational field of the Earth does not vary around the surface. ...........................................................
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3 (a) Define specific heat capacity.
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(b) A block of aluminium has a volume of $3.612 \times 10^{-3} \, \text{m}^3$ at a temperature of $0^\circ \text{C}$ .
Aluminium has a density of $2.700 \times 10^3 \, \text{kg} \, \text{m}^{-3}$ at $0^\circ \text{C}$ .
It has a density of $2.620 \times 10^3 \, \text{kg} \, \text{m}^{-3}$ at $500^\circ \text{C}$ .
The block is heated so that*0000800000009* DFD 9 (iv) Explain whether the work done on the block is positive or negative. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (v) Use the first law of thermodynamics to determine, to three significant figures, a value for the specific heat capacity of aluminium. Explain your reasoning. Give a unit with your answer. specific heat capacity = ........................................ unit ............... [3] (c) Without further calcul
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4 (a) The equation of state for an ideal gas may be written as
$$
pVA = NBT
$$
where $p$ is the pressure of the gas, $V$ is the volume of the gas, $A$ is the Avogadro constant, $B$ is another constant and $N$ is the number of molecules of the gas.
(i) State the meaning, in the equation, of the symbol $T$ .
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(ii) Identify the constant $B$ .
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(b) The product $pV$ for an ideal gas is also given by
$$
pV = \frac{1}{3}Nm\langle c^2\rangle.
$$
(i) State the meanings, in this equation, of the symbols $m$ and $\langle c^2\rangle$*0000800000011* DFD 11 (c) On Fig. 4.1, sketch the variation with $T$ of the root-mean-square (r.m.s.) speed of the molecules of an ideal gas.  Fig. 4.1 2 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 © UCLES 2025 9702/42/M/J/25 [Turn over] r.m.s. speed $\uparrow$ $0 \quad T \rightarrow$ 0
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5 (a) State what is meant by simple harmonic motion.
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(b) A block is suspended by a spring. The block oscillates vertically with simple harmonic motion.
The velocity $v$ of the block varies with time $t$ according to
$$
v = 0.56 \cos 16t
$$
where $v$ is in m s $^{-1}$ and $t$ is in s.
(i) Calculate the period of the oscillation.
period = ......................................*0000800000013* DFD 13 (iv) On Fig. 5.1, sketch the variation of $v$ with $x$. <div style="text-align: center;">  </div> Fig. 5.1 3 © UCLES 2025 9702/42/M/J/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** --- **v/ms⁻¹** -6 -4 -2 0 2 4 6 **x/cm** -0.8 -0.4 0 0.4 0.8 [3] [Total: 9]
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6 Two parallel metal plates X and Y are separated by a distance of 0.041 m, as shown in Fig. 6.1.
<div style="text-align: center;">
</div>
Fig. 6.1
There is a vacuum between the plates. An electron is at rest at the centre of plate X.
A potential difference (p.d.) of 58 kV is applied across the plates. This causes the electron to accelerate towards plate Y.
(a) On Fig. 6.1, use the symbols + and – to indicate which of plates X and Y is the positive plate and which is the negative plate. [1]
(b) (i) Calculate the electric field strength $E$ between the plates. Give a unit with your answer.
$$
E = \underline{\hspace{3cm}} \text{ unit } \underline{\hspace{3cm}} \quad [2]
$$
(ii) Determine the acceleration of the electron.
$$
\text{a*0000800000015* DFD 15 (c) Many electrons are now accelerated from rest from plate X to plate Y in Fig. 6.1. When the electrons hit plate Y, the absorption of their kinetic energies results in the emission of electromagnetic waves. (i) Show that the minimum wavelength of these electromagnetic waves is 21 pm. [3] (ii) State the region of the electromagnetic spectrum that contains these waves. ................................................................................................................... [1] (iii) Explain how these electromagnetic waves may be used to form images of internal body structures. ................................................................................................................... .........................................................
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7 Fig. 7.1 shows a circuit containing a capacitor of capacitance $C$ and a resistor of resistance $R$ .
<div style="text-align: center;">
</div>
Fig. 7.1
Initially, the switch is open and the potential difference (p.d.) across the capacitor is 12 V.
The switch is closed at time $t = 0$ and the capacitor discharges through the resistor.
Fig. 7.2 shows the variation of the charge $Q$ on the capacitor with the p.d. $V_C$ across the capacitor as the capacitor discharges. Fig. 7.3 shows the variation of the current $I$ in the resistor with the p.d. $V_R$ across the resistor as the capacitor discharges.
<div style="display: flex; justify-content: space-between;">
<div>
<p>Fig. 7.2</p>
</div>
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(ii) the resistance $R$ , in k $\Omega$
$$
R = \underline{\hspace{5cm}} \text{ k}\Omega \ [2]
$$
(iii) the time constant $\tau$ of the circuit.
$$
\tau = \underline{\hspace{5cm}} \text{ s } [2]
$$
(c) Use Fig. 7.2, Fig. 7.3 and your answer in (a) to explain why the variation of $Q$ with $t$ is exponential in nature.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}} \ [3]$
[Total: 10]
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Note: The vertical text "DO NOT WRITE IN THIS MARGIN" on the left margin is not included in the Markdown as it is a formatting instruction and not part of the main content. If you need it included, please let me know.*0000800000018*
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8 Fig. 8.1 shows a circuit that produces rectification of an alternating input voltage.
<div style="text-align: center;">
</div>
Fig. 8.1
The input voltage $V_{IN}$ is sinusoidal. The rectified output voltage $V_{OUT}$ is applied across resistor R.
The variation of $V_{IN}$ with time $t$ has amplitude $V_0$ and period $T$, as shown in Fig. 8.2.
<div style="text-align: center;">
</div>
Fig. 8.2
The root-mean-square (r.m.s.) value of $V_{IN}$ is 6.0 V.
(a) (i) State the type of rectification produced by the circuit of Fig. 8.1.
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(ii) Calculate $V_0$.
$$
V_0 = \text{......................*0000800000019*
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(b) Resistor R has resistance $45\,\Omega$ .
Assume that there is no p.d. across the diode when it is conducting.
(i) Determine the peak power $P_0$ in the resistor.
$$
P_0 = \underline{\hspace{6cm}} \text{ W [2]}
$$
(ii) On Fig. 8.3, sketch the variation of the power $P$ in the resistor with $t$ between $t = 0$ and $t = 2T$ .
Fig. 8.3
[3]
(iii) Use the answer in (b)(ii) to explain why the mean power in the resistor is $\frac{1}{4}P_0$ .
$\underline{\hspace{6cm}}$
$\underline{\hspace{6cm}}$
$\underline{\hspace{6cm}}$ [2]
(iv) Use the information in (b)(iii) to determine the r.m.s. value of $V_{\text{OUT}}$ .
r.m.s. voltage = $\underline{\hspace{6cm}} \text{ V 1}$
© UCLES 2025
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Note: The vertical text "DO NOT WRITE IN THIS *0000800000020* DFD 20 9 (a) State what is meant by the photoelectric effect. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) The photoelectric effect is investigated in two stages using the circuit shown in Fig. 9.1. metal plate electromagnetic radiation, frequency $f$ polished metal plate vacuum X Y A V P Fig. 9.1 The polished metal plate Y is illuminated with electromagnetic radiation of frequency $f$ and constant power. In stage
*0000800000021* DFD 21 (i) Explain, with reference to photons, why $V_S$ depends on the frequency of the incident electromagnetic radiation. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (ii) S
*0000800000022* DFD 22 10 (a) Radioactive decay is a spontaneous process. State the meaning, in this context, of the term spontaneous. ............................................................................................................................... ............................................................................................................................... [1] (b) Two radioactive isotopes X and Y each decay to form a stable isotope. A sample initially contains only atoms of isotope X. At this time, its activity is $4A$. Another sample initially contains only atoms of Y. At this time, its activity is $A$. Fig. 10.1 shows the variation of the activity of each sample with time $t$ between $t = 0$ and $t = 6T$.  Fig. 10.1 (i)
*0000800000023* DFD 23 (ii) Determine, in terms of $T$, the time at which the two samples will have equal activities. time = ………………………………………… $T$ [3] (c) A radiation detector is placed near to one of the samples in (b). Explain why the count rate measured by the detector is less than the activity of the sample. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 2 © UCLES 2025 9702/42/M/J/25