科目：物理 Physics (9702)
年份：2025 冬季
试卷：Paper 44
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
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1 (a) State Newton’s law of gravitation.
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(b) A binary star consists of star A, of mass $4.0 \times 10^{30} \text{kg}$ , and star B, of mass $2.0 \times 10^{30} \text{kg}$ , separated by a distance of $3.3 \times 10^{12} \text{m}$ . The stars are both in circular orbit around their common centre of gravity X, as shown in Fig. 1.1.
<div style="text-align: center;">
 Calculate the centripetal acceleration of star A.
acceleration = ………………………………………… m s⁻² [1]
(iii) Use your answer in (b)(ii) to determine the period of the orbit of star A.
period = ………………………………………… s [3]
(iv) By placing a tick (√) in each row, complete Table 1.1 to show how the quantities indicated for star B compare with the same quantities for star A.
Table 1.1
<table>
<tr>
<th></th>
<th>B less than A</th>
<th>B equal to A</th>
<th>B greater than A</th>
</tr>
<tr>
<td>centripetal acceleration</td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>linear speed</td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>period</td>
<td></td>
<td></td>
<td></td>
</tr>
</table>
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© UCLES 2*0000800000006* DFD 6 2 (a) The equation of state for an ideal gas may be expressed as $$ pV = NkT. $$ (i) State the meaning of each of the symbols in this equation. $p$: ............................................................................................................... $V$: ............................................................................................................... $N$: ............................................................................................................... $k$: ............................................................................................................... $T$: ............................................................................................................... [3] (ii) Using the equation of state,
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(b) A molecule of hydrogen gas consists of two hydrogen atoms, each of nucleon number 1.
A molecule of oxygen gas consists of two oxygen atoms, each of nucleon number 16.
Assume that hydrogen and oxygen both behave as ideal gases.
A sample of hydrogen gas is at the same temperature as a sample of oxygen gas.
For the two samples, determine the ratio
$$
\frac{\text{root-mean-square (r.m.s.) speed of hydrogen molecules}}{\text{root-mean-square (r.m.s.) speed of oxygen molecules}}
$$
ratio = ………………………………………… 2
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3 (a) With reference to molecular kinetic energy and molecular potential energy, explain what is meant by the internal energy of an ideal gas.
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(b) A sample of an ideal gas is initially in state A, at a pressure of $2.0 \times 10^5$ Pa and with a volume of $0.016 \, \text{m}^3$ , as shown in Fig. 3.1.
Fig. 3.1
In state A, the temperature of the gas is 400 K*0000800000009* DFD 9 (i) Determine the internal energy of the gas in state A. internal energy = ………………………………………… J [2] (ii) Determine the temperature of the gas in state B. temperature = ………………………………………… K [1] (iii) Determine the volume of the gas in state C. volume = ………………………………………… m³ [1] (iv) On Fig. 3.1, draw two lines, one to represent change X and one to represent change Y. Label your lines X and Y respectively. 3 © UCLES 2025 9702/44/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
*0000800000010* DFD 10 4 (a) State what is meant by the frequency of the oscillations of an oscillating object. ............................................................................................................................... ............................................................................................................................... [1] (b) An object is oscillating. Fig. 4.1 shows the variation of the acceleration $a$ of the object with its displacement $x$ from the equilibrium position. Fig. 4.2 shows the variation of the kinetic energy $E_K$ of the object with time $t$ . <div style="display: flex; justify-content: space-between;"> <div style="width: 45%;"> **Fig. 4.1**  </div> <div style="width: 45%;"> **Fig. 4.2** ![i
*0000800000011* DFD 11 (iii) Apart from the period, frequency and angular frequency of the oscillations, determine **three** other conclusions about the object and its oscillations that may be drawn from Fig. 4.1 and Fig. 4.2. The conclusions may be qualitative or quantitative. Use the space below for any working. 1 ....................................................................................................................... .................................................................................................................... 2 ....................................................................................................................... ....................................................................................................................
*0000800000012* DFD 12 5 (a) Explain why the electric potential near an isolated proton is positive. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) An isolated metal sphere is positively charged and has radius $R$, as shown in Fig. 5.1. <!-- Image: Fig. 5.1 --> Fig. 5.1 Line XY passes through the centre of the sphe
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(ii) On Fig. 5.2, sketch the variation of the electric field $E$ at point P with $x$ for values of $x$ between $x = -3R$ and $x = 3R$ . Do not include the region inside the sphere between $x = -R$ and $x = R$ .
<div style="text-align: center;">
</div>
Fig. 5.2
[3]
(c) The proton and the electron in a hydrogen atom are separated by a distance of $5.3 \times 10^{-11}$ m.
Calculate the electric potential energy of the proton and the electron.
electric potential energy = ______________________________ J 2
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6 Fig. 6.1 shows part of a bridge rectifier circuit that can be used for rectification of an alternating input voltage $V_{IN}$.
<div style="text-align: center;">
</div>
Fig. 6.1
The circuit contains four diodes, one of which is shown.
The rectified output voltage $V_{OUT}$ is applied across load resistor R.
(a) (i) State what is meant by rectification.
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(ii) State the name of the type of rectification produced by a bridge rectifier circuit.
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(iii) Complete the circuit in Fig. *0000800000016*
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(b) The input voltage varies with time $t$ according to the equation
$$
V_{IN} = 34 \sin 18t
$$
where $V_{IN}$ is in V and $t$ is in s.
(i) Show that the period of the input voltage is 0.35 s.
[2]
(ii) Calculate the root-mean-square (r.m.s.) input voltage.
r.m.s. voltage = ………………………………………… V [1]
(iii) On Fig. 6.2, sketch the variation of $V_{OUT}$ with $t$ from $t = 0$ to $t = 0.35$ s.
Fig. 6.2
[3]
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(c) Resistor R has a resistance of $56\,\text{k}\Omega$ . A capacitor of capacitance $12\,\mu\text{F}$ is connected into the circuit of Fig. 6.1 in order to smooth the output voltage.
(i) On Fig. 6.1, draw the capacitor correctly connected into the circuit. [1]
(ii) Calculate the time constant of the smoothing circuit.
time constant = ………………………………………… s [2]
(iii) During each discharge cycle, the time for which the capacitor is discharging is $0.14\,\text{s}$ .
Determine the minimum value of the smoothed output voltage.
minimum voltage = ………………………………………… V 2
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7 (a) State Lenz’s law of electromagnetic induction.
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(b) A helicopter hovering in stationary equilibrium has four rotors, each of length 12 m, as shown in the view from above in Fig. 7.1.
<div style="text-align: center;">
</div>
Fig. 7.1
The vertical component of the Earth’s magnetic field at the helicopter is downwards with a flux density of 0.047 mT*0000800000019*
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(ii) Determine the magnitude of the electromotive force (e.m.f.) induced across the length of rotor OX.
$$
\text{e.m.f.} = \underline{\hspace{5cm}} \text{ V [2]}
$$
(iii) Use Lenz’s law to explain whether end O or end X of the rotor is at the higher potential.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{5cm}}$ [2]
[Total: 9]
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8 Oxygen-15 ( $^{15}_{8}\text{O}$ ) is radioactive and has a half-life of 2.04 minutes.
The decay of oxygen-15 produces positrons. For this reason, oxygen-15 is sometimes used as a tracer in positron emission tomography (PET scanning).
(a) State what is meant by a tracer.
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(b) The equation for the decay of oxygen-15 is
$$
^{15}_{8}\text{O} \rightarrow {}_{Q}^{P}\text{X} + {}_{S*0000800000021*
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(iii) Determine the rate at which positrons are produced in a sample of oxygen-15 that has a mass of $2.85 \times 10^{-6}$ kg.
rate = ………………………………………… s⁻¹ [4]
(d) The particles that are emitted from the body and detected outside it during PET scanning are not positrons but another type of particle.
(i) State the name of the particles that are detected.
……………………………………………………………………………………………………… [1]
(ii) Explain how these particles are formed inside the body.
……………………………………………………………………………………………………
……………………………………………………………………………………………………
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……………………………………………………………………………………………………… 2
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Note: The vertical text "DO NOT WRITE IN THIS MARGIN" on the left margin is not included in the Markdo*0000800000022* DFD 22 9 (a) State what is meant by the photoelectric effect. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) The photoelectric effect is investigated using two clean metal plates. One plate is made from metal X and the other is made from metal Y. Metal X has work function energy $\phi$ . Metal Y has work function energy $2\phi$ . Metal X has threshold frequency $F$ . State expressions, in terms of either or both of $\phi$ and
*0000800000023* DFD 23 10 (a) State what is meant by redshift. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Explain how observations of redshift lead to the idea that the universe is expanding. ............................................................................................................................... ..........................................................................................................................