科目：物理 Physics (9702)
年份：2024 冬季
试卷：Paper 43
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.
[2]
(b) A planet may be considered as a uniform sphere.
A satellite is in circular orbit of period $ T $ around the planet at a height $ h $ above the surface. The height of the orbit can be adjusted by use of the satellite's rocket engines.
Fig. 1.1 shows the variation with $ h $ of $ T^{\frac{2}{3}} $ .
(i) By reference to forces, explain why the orbit of the satellite is circular.
[2]
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(ii) Use Newton's law of gravitation to show that $ h $ and $ T $ are related by
$$
(h + B)^3 = \frac{GA}{4\pi^2}T^2
$$
where $ G $ is the gravitational constant and $ A $ and $ B $ are constants that depend on the properties of the planet.
[3]
(iii) Use the gradient and intercept of the line in Fig. 1.1 to determine values for $ A $ and $ B $ . Give units with your answers.
$ A = \ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots $ unit $\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots$
$ B = \ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots $ unit $\ldots\ldots\ldots\ldots\ldots\ldots\ldo*0000800000006*
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2 (a) Define specific heat capacity.
[2]
(b) Two solid blocks X and Y are made from different metals. The blocks have different initial temperatures. Block Y is initially at room temperature.
The blocks are placed in direct thermal contact with each other at time $ t = 0 $. Fig. 2.1 shows the variation with $ t $ of the temperatures of the two blocks.
Fig. 2.1
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**Figure 2.1**
<table>
<thead>
<tr>
<th>Temperature (°C)</th>
<th>t (min)</th>
</tr>
</thead>
<tbody>
<tr>
<td>0</td>
<td>0</td>
</tr>
<tr>
<td>25</td>
<td*0000800000007* DO NOT WRITE IN THIS MARGIN 7 (i) State three conclusions that may be drawn from Fig. 2.1. The conclusions may be qualitative or quantitative. 1 ....................................................................................................................... .................................................................................................................... 2 ....................................................................................................................... .................................................................................................................... 3 ....................................................................................................................... ................................
*0000800000008* 8 3 (a) (i) State what is meant by the Avogadro constant. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [1] (ii) State the relationship between the Avogadro constant $N_A$, the molar gas constant $R$ and the Boltzmann constant $k$. [1] (b) Two samples X and Y of ideal gases are both at thermodynamic temperature $T$. Sample X has volume $V$ and consists of $N$ molecules, each of mass $m$. Sample Y has volume $2V$ and consists of $2N
*0000800000009* DO NOT WRITE IN THIS MARGIN 9 (ii) The temperature of sample X is now varied. On Fig. 3.1, sketch the variation with thermodynamic temperature of the root-mean-square (r.m.s.) speed of the molecules of the gas. r.m.s. speed ↑ 0 → thermodynamic temperature Fig. 3.1 2 DO NOT WRITE IN THIS MARGIN © UCLES 2024 9702/43/O/N/24 [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
*0000800000010* 10 4 (a) State what is meant by simple harmonic motion. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A block is suspended from a spring, as shown in Fig. 4.1.  Fig. 4.1 The block is pulled down and released at time $t = 0$. It then oscillates vertically with simple harmonic motion. Fig. 4.2 shows the variation of the velocity $v$ of the block with height $h$ of the base of the block above the floor. ![
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(i) Determine the amplitude, in cm, of the oscillations.
amplitude = ………………………………………… cm [1]
(ii) Show that the angular frequency of the oscillations is $3.2 \text{ rad} \text{s}^{-1}$ .
[2]
(iii) Calculate the period $T$ of the oscillations.
$T =$ ………………………………………… s [2]
(iv) On Fig. 4.3, sketch the variation of $h$ with time $t$ from $t = 0$ to $t = 6.0 \text{ s}$ .
Fig. 4.3
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DO NOT WRITE IN THIS MARGIN*0000800000012* 12 5 (a) State the relationship between electric field and electric potential. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Two charged isolated insulating spheres X and Y are near to each other, as shown in Fig. 5.1. X P Y Fig. 5.1 P is a point on the line joining the centres of the spheres. Explain why it is **not** possible for the total electric potential and the resultant electric field to simultaneously be zero at p
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(ii) State an expression, in terms of $Q$ , $x$ and the permittivity of free space $\varepsilon_0$ , for the electric field strength $E_x$ at P due to sphere X.
$$
E_x = \text{..................................................} [1]
$$
(iii) Determine an expression, in terms of $Q$ , $x$ and $\varepsilon_0$ , for the resultant electric field strength $E$ at point P due to the two spheres.
$$
E = \text{..................................................} 2
$$
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DO NOT WRITE IN THIS MARGIN*0000800000014* 14 6 (a) (i) State what is meant by rectification of an alternating voltage. ............................................................................................................................... ............................................................................................................................... [1] (ii) State the difference between half-wave rectification and full-wave rectification. ............................................................................................................................ ............................................................................................................................ [2] (b) (i) Complete Fig. 6.1 to show a circuit that produces half-wave rectification of an alternatin
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Fig. 6.3 shows the variation of $V_{OUT}$ with $t$ .
Fig. 6.3
The maximum energy stored in the capacitor is 0.041 J.
(i) Show that the capacitance of C is 570 $\mu$ F.
[2]
(ii) Determine the resistance of R.
resistance = ………………………………………… $\Omega$ 3
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DO NOT WRITE IN THIS MARGIN*0000800000016* 16 7 (a) Define magnetic flux density. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A long, straight wire carries a current into the page, as shown in Fig. 7.1. $\otimes$ Fig. 7.1 On Fig. 7.1, draw four field lines to represent the magnetic field around the wire due to the current in it. [3] (c) Two identical wires X and Y are placed parallel to each other. The wires both carry current into the page, as shown in Fig. 7.2.
*0000800000017* DO NOT WRITE IN THIS MARGIN 17 (i) Explain why the two wires exert a magnetic force on each other. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) On Fig. 7.2, draw an arrow to show the direction of the magnetic force exerted on wire X. Label your arrow F. [1] (iii) The current in X is double the curr
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8 A polished sheet of magnesium in a vacuum emits electrons when it is illuminated by ultraviolet radiation.
(a) State the name of this phenomenon.
[1]
(b) For emission of electrons to occur, the frequency of the ultraviolet radiation must be at least $8.8 \times 10^{14}$ Hz.
(i) Calculate the work function energy of magnesium.
work function energy = J [2]
(ii) For ultraviolet radiation with a frequency of $11 \times 10^{14}$ Hz, calculate the maximum speed of the emitted electrons.
maximum speed = m s $^{-1}$ [3]
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(c) The frequency $ f $ of the ultraviolet radiation incident on the magnesium sheet is varied between $ 8.0 \times 10^{14} $ Hz and $ 11 \times 10^{14} $ Hz.
On Fig. 8.1, sketch the variation with $ f $ of the maximum kinetic energy $ E_{MAX} $ of the emitted electrons. Use the space below for any working that you need.
Fig. 8.1
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9 Fluorine-18 ( $^{18}_{9}\text{F}$ ) decays by beta-plus ( $\beta^+$ ) emission with a half-life of 110 minutes.
(a) (i) State the name of the beta-plus particle.
[1]
(ii) Show that the decay constant of fluorine-18 is $1.05 \times 10^{-4} \, \text{s}^{-1}$ .
[1]
(iii) Determine the activity of $2.1 \times 10^{-12} \, \text{kg}$ of fluorine-18.
activity = ……………………………………… Bq [3]
(b) A small sample of fluorine-18 injected into the body acts as a tracer for use in medical imaging.
(i) Describe how the interaction of a $\beta^+$ particle with an electron in the body enables the formation of an image.
[3]
(ii) Suggest why 110 minutes is a suitable half-life for a nuclide used as a tracer in medical diagnosis.
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10 (a) Explain how redshift leads to the idea that the Universe is expanding.
[3]
(b) Stars in a distant galaxy emit radiation. The total luminosity of the stars in the galaxy is $1.90 \times 10^{36} W$ . The emission spectrum of the radiation contains a line X at a wavelength of 658 nm.
Radiation from the galaxy is observed on the Earth. The observed radiation has a radiant flux intensity of $8.42 \times 10^{-16} W m^{-2}$ . In the observed emission spectrum, line X is at a wavelength of 726 nm.
Determine:
(i) the distance $d$ of the galaxy from the Earth
$d = \text{m [2]}$
(ii) the speed $v$ of the galaxy relative to the Earth.
$v = \text{m s}^{-1} \text{[2]}$
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DO NOT WRITE I*0000800000023* 23 (c) Observations of many galaxies, such as the one in (b), lead to many pairs of values of $ d $ and $ v $ . Plotting these values reveals a trend. (i) On Fig. 10.1, sketch the variation of $ v $ with $ d $ .  Fig. 10.1 [2] (ii) State the name of the quantity represented by the gradient of the line in Fig. 10.1. ............................................................................................................................... 1 © UCLES 2024 9702/43/O/N/24