科目：物理 Physics (9702)
年份：2022 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, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics, 25: Astronomy and cosmology
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1 (a) (i) Define gravitational potential at a point.
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(ii) Starting from the equation for the gravitational potential due to a point mass, show that the gravitational potential energy $E_p$ of a point mass $m$ at a distance $r$ from another point mass $M$ is given by
$$
E_p = -\frac{GMm}{r}
$$
where $G$ is the gravitational constant.
[1]
(b) Fig. 1.1 shows the path of a comet of mass $2.20 \times 105
Both the comet and the star can be considered as point masses at their centres.
(i) Calculate the magnitude of the change in the gravitational potential energy $\Delta E_p$ of the comet as it moves from position X to position Y.
$$
\Delta E_p = \underline{\hspace{5cm}} \text{ J [2]}
$$
(ii) State, with a reason, whether the change in gravitational potential energy in (b)(i) is an increase or a decrease.
$\underline{\hspace{10cm}}$ [1]
(iii) Use your answer in (b)(i) to determine the speed, in km s $^{-1}$ , of the comet at point Y.
$$
\text{speed} = \underline{\hspace{5cm}} \text{ km s}^{-1} \text{ [3]}
$$
(c) A second comet passes point X with the same speed as the comet in (b) and travelling in the same direction. This comet is gradually losing mass. The mass of this comet when6 2 (a) State Coulomb’s law. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Positronium is a system in which an electron and a positron orbit, with the same period, around their common centre of mass, as shown in Fig. 2.1. <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <center> <cente
7 (iii) Use the information in (b)(ii) to determine the period of the circular orbit of the two particles. period = ………………………………………… s [3] (c) Positronium is highly unstable, and after a very short period of time it becomes gamma radiation. (i) Describe how gamma radiation is formed from the two particles in positronium. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… [3] (ii) State one medical application of the process described in (c)(i). ……………………………………………………………………………………………………… 1 © UCLES 2022 9702/42/M/J/22 [Turn over
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3 (a) Define specific latent heat of vaporisation.
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(b) The specific latent heat of vaporisation of water at atmospheric pressure of $1.0 \times 10^5$ Pa is $2.3 \times 10^6$ J kg $^{-1}$ . A mass of 0.37 kg of liquid water at 100 °C is provided with the thermal energy needed to vaporise all of the water at atmospheric pressure.
(i) Calculate the thermal energy $q$ supplied to the water.
$q = \underli9 (iv) Use your answers in (b)(i) and (b)(iii) to determine the increase in internal energy of the water when it vaporises at 100°C. Explain your reasoning. increase in internal energy = ………………………………………… J [2] (c) Use the first law of thermodynamics to suggest, with a reason, how the specific latent heat of vaporisation of water at a pressure greater than atmospheric pressure compares with its value at atmospheric pressure. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… 2 © UCLES 2022 9702/42/M/J/22 [Turn over
10 4 (a) State what is meant by resonance. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Fig. 4.1 shows a heavy pendulum and a light pendulum, both suspended from the same piece of string. This string is secured at each end to fixed points. <div style="text-align: center;">  </div> Fig. 4.1 Both pendulums have the same natural frequency. The heavy pendulum is set oscillating perpendicular to the plane of the diagram.
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The variation with $t$ of the displacement $x$ of the light pendulum is given by
$$
x = 0.25 \sin 5.0\pi t
$$
where $x$ is in centimetres and $t$ is in seconds.
(i) Calculate the period $T$ of the oscillations.
$$
T = \underline{\hspace{5cm}} \text{ s [2]}
$$
(ii) On Fig. 4.2, label both of the axes with the correct scales. Use the space below for any additional working that you need.
$$
\text{[2]}
$$
(iii) Determine the magnitude of the phase difference $\phi$ between the oscillations of the light and heavy pendulums. Give a unit with your answer.
$$
\phi = \underline{\hspace{5cm}} \text{ unit } \underline{\hspace{5cm}} \text{ [2]}
$$
[Total: 8]
© UCLES 2022 9702/42/M/J/22 [Turn over12 5 (a) Define the capacitance of a parallel plate capacitor. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Two capacitors, of capacitances $C_1$ and $C_2$, are connected in parallel to a power supply of electromotive force (e.m.f.) $E$, as shown in Fig. 5.1. <div style="text-align: center;">  <br/> Fig. 5.1 </div> Show that the combined capacitance $C_T$ of the two capacitors is given by $$ C_T = C_1 + C_2. $$ Ex
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(c) Two capacitors of capacitances $22\,\mu\text{F}$ and $47\,\mu\text{F}$ , and a resistor of resistance $2.7\,\text{M}\Omega$ , are connected into the circuit of Fig. 5.2.
Fig. 5.2
The battery has an e.m.f. of $12\,\text{V}$ .
(i) Show that the combined capacitance of the two capacitors is $15\,\mu\text{F}$ .
[1]
(ii) The two-way switch S is initially at position X, so that the capacitors are fully charged. Use the information in (c)(i) to calculate the total energy stored in the two capacitors.
total energy = ………………………………………… J [2]
(iii) The two-way switch is now moved to position Y.
Determine the time taken for the potential difference (p.d.) across the $22\,\mu\text{F}$ capacitor to become $6.0\,\text{V}$ .
time = ………………………………………… s 3
© UCLES 2022 9702/42/M/J/22 [Total: 14 6 (a) State the two conditions that must be satisfied for a copper wire, placed in a magnetic field, to experience a magnetic force. 1 ............................................................................................................................... ............................................................................................................................... 2 ............................................................................................................................... ............................................................................................................................... [2] (b) A long air-cored solenoid is connected to a power supply, so that the solenoid creates a magnetic field. Fig. 6.1 shows a cross-secti
15 (c) Two long parallel current-carrying wires are placed near to each other in a vacuum. Explain why these wires exert a magnetic force on each other. You may draw a labelled diagram if you wish. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... 3 © UCLES 2022 9702/42/M/J/22 [Turn over
16 7 (a) State Faraday’s law of electromagnetic induction. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Two coils are wound on an iron bar, as shown in Fig. 7.1.  Fig. 7.1 Coil 1 is connected to a potential difference (p.d.) $V_1$ that gives rise to a magnetic field in the iron bar. Fig. 7.2 shows the variation with time $t$ of the magnetic flux density $B$ in the iron bar.  Fig. 7.2 A voltmeter
17 On Fig. 7.3, sketch the variation with $t$ of $V_2$ between $t = 0$ and $t = 0.40$ s. $\uparrow$ $V_2$ 0 0.1 0.2 0.3 $t/s$ 0.4 Fig. 7.3 [4] (c) Coil 2 in (b) is now replaced with a copper ring that rests loosely on top of coil 1. The supply to coil 1 is replaced with a cell and a switch that is initially open, as shown in Fig. 7.4. iron bar copper ring coil 1 Fig. 7.4 (i) The switch is now closed. As it is closed, the copper ring is observed to jump upwards. Explain why this happens. ............................................................................................................................... ............................................................................................................................... .....................................
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8 (a) State one piece of experimental evidence for:
(i) the particulate nature of electromagnetic radiation
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(ii) the wave nature of matter.
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(b) (i) Calculate the de Broglie wavelength $\lambda$ of an alpha-particle moving at a speed of $6.2 \times 10^7 \, \text{m} \, \text{s}^{-1}$ .
$\lambda = \underline{\hspace{5cm}} \, \text{m} \, [3]$
(ii) The speed $v$ of the alpha-particle in (b)(i) is gradually reduced to zero.
On Fig. 8.1, sketch the variation with $v$ of $\lambda$ .
$\begin{array}{c}
\uparrow \\
\lambda \\
\downarrow \\
0 \quad \qua19 9 (a) (i) State Hubble’s law. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) Explain how cosmologists use observations of emission spectra from stars in distant galaxies to determine that the Universe is expanding. ............................................................................................................................... .....................................................................................................
20 10 (a) State what is meant by radioactive decay. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A radioactive sample consists of an isotope X of half-life $T$ that decays to form a stable product. Only X and the stable product are present in the sample. At time $t = 0$, the sample has an activity of $A_0$ and contains $N_0$ nuclei of X. (i) On Fig. 10.1, sketch the variation with $t$ of the number $N$ of nuclei of X present in the sample. Yo
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(ii) On Fig. 10.2, sketch the variation with $N$ of the activity $A$ of the sample for values of $N$ between $N = 0$ and $N = N_0$ .
Fig. 10.2
[2]
(c) State the name of the quantity represented by the gradient of your line in:
(i) Fig. 10.1
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(ii) Fig. 10.2.
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(d) For the sample in (b), calculate the fraction $\frac{N}{N_0}$ at time $t = 1.70T$ .
$$
\frac{N}{N_0} = \text{................................................................................................................... [2]}
$$
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