科目：物理 Physics (9702)
年份：2014 冬季
试卷：Paper 42
总页数：24
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 18: Electric fields, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
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Section A
Answer all the questions in the spaces provided.
1 An isolated spherical planet has a diameter of $6.8 \times 10^6$ m. Its mass of $6.4 \times 10^{23}$ kg may be assumed to be a point mass at the centre of the planet.
(a) Show that the gravitational field strength at the surface of the planet is $3.7 \, \text{N} \, \text{kg}^{-1}$ .
[2]
(b) A stone of mass 2.4 kg is raised from the surface of the planet through a vertical height of 1800 m.
Use the value of field strength given in (a) to determine the change in gravitational potential energy of the stone.
Explain your working.
change in energy = ………………………………………… J [3]
(c) A rock, initially at rest at infinity, moves towards the planet. At point P, its height above the surface of the planet is $3.5D$ , where $D$ is the 5 Calculate the speed of the rock at point P, assuming that the change in gravitational potential energy is all transferred to kinetic energy. speed = ………………………………………… m s⁻¹ [4] © UCLES 2014 9702/42/O/N/14 [Turn over
6 2 A large bowl is made from part of a hollow sphere. A small spherical ball is placed inside the bowl and is given a horizontal speed. The ball follows a horizontal circular path of constant radius, as shown in Fig. 2.1. Fig. 2.1 The forces acting on the ball are its weight $W$ and the normal reaction force $R$ of the bowl on the ball, as shown in Fig. 2.2. Fig. 2.2 The normal reaction force $R$ is at an angle $\theta$ to the horizontal. (a) (i) By resolving the reaction force $R$ into two perpendicular components, show that the resultant force $F$ acting on the ball is given by the expression $$ W = F \tan \theta. $$ [2] © UCLES 2014 9702/42/O/N/14
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(ii) State the significance of the force $F$ for the motion of the ball in the bowl.
............................................................................................................................ [1]
(b) The ball moves in a circular path of radius 14 cm. For this radius, the angle $\theta$ is $28^\circ$ .
Calculate the speed of the ball.
speed = ........................................... m s $^{-1}$ [3]
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3 (a) State what is meant by an *ideal gas*.
...............................................................................................................................
............................................................................................................................... [1]
(b) A storage cylinder for an ideal gas has a volume of $3.0 \times 10^{-4} \, \text{m}^3$ . The gas is at a temperature of $23^\circ \text{C}$ and a pressure of $5.0 \times 10^7 \, \text{Pa}$ .
(i) Show that the amount of gas in the cylinder is 6.1 mol.
[2]
(ii) The gas leaks slowly from the cylinder so that, after a time of 35 days, the pressure has reduced by 0.40%. The temperature remains constant.
Calculate the average rate, in atoms per second, at which gas atoms escape fro10
4 (a) State what is meant by *simple harmonic motion*.
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............................................................................................................................... [2]
(b) A small ball rests at point P on a curved track of radius $r$ , as shown in Fig. 4.1.
<div style="text-align: center;">
</div>
Fig. 4.1
The ball is moved a small distance to one side and is then released. The horizontal displacement $x$ of the ball is related to its acceleration $a$ towards P by the expression
$$
11 (c) The variation with time $t$ of the displacement $x$ of the ball in (b) is shown in Fig. 4.2. Fig. 4.2 Some moisture now forms on the track, causing the ball to come to rest after approximately 15 oscillations. On the axes of Fig. 4.2, sketch the variation with time $t$ of the displacement $x$ of the ball for the first two periods after the moisture has formed. Assume the moisture forms at time $t = 0$. [3] © UCLES 2014 9702/42/O/N/14 [Turn over
12 5 (a) Define *electric potential* at a point. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) An isolated solid metal sphere is positively charged. The variation of the potential $V$ with distance $x$ from the centre of the sphere is shown in Fig. 5.1.  Fig. 5.1 Use Fig. 5.1 to suggest (i) why the radius of the sphere cannot be greater than 1.0 cm, ......................................................................
13 (ii) that the charge on the sphere behaves as if it were a point charge. [3] (c) Assuming that the charge on the sphere does behave as a point charge, use data from Fig. 5.1 to determine the charge on the sphere. charge = ………………………………………… C [2] © UCLES 2014 9702/42/O/N/14 [Turn over
14 BLANK PAGE © UCLES 2014 9702/42/O/N/14
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6 A stiff straight copper wire XY is held fixed in a uniform magnetic field of flux density $2.6 \times 10^{-3} \text{T}$ , as shown in Fig. 6.1.
<div style="text-align: center;">
</div>
Fig. 6.1
The wire XY has length 4.7 cm and makes an angle of $34^\circ$ with the magnetic field.
(a) Calculate the force on the wire due to a constant current of 5.4 A in the wire.
force = ………………………………………… N [2]
(b) The current in the wire is now changed to an alternating current of r.m.s. value 1.7 A.
Determine the total variation in the force on the wire due to the alternating current.
variation in force = ………………………………………… N [3]
© UCLES 2014 9702/42/O/N/14 [Turn over16 7 (a) The mean value of an alternating current is zero. Explain (i) why an alternating current gives rise to a heating effect in a resistor, ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) by reference to heating effect, what is meant by the root-mean-square (r.m.s.) value of an alternating current. ............................................................................................................................... ..............
17 (ii) Use Faraday’s law to explain why the current in the primary coil is not in phase with the e.m.f. induced in the secondary coil. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] © UCLES 2014
18 8 White light is incident on a cloud of cool hydrogen gas, as illustrated in Fig. 8.1. <div style="text-align: center;">  </div> Fig. 8.1 The spectrum of the light emerging from the gas cloud is found to contain a number of dark lines. (a) Explain why these dark lines occur. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... .........................................................................................................
19 One dark line is observed at a wavelength of 435 nm. (i) Calculate the energy, in eV, of a photon of light of wavelength 435 nm. energy = ………………………………………… eV [4] (ii) On Fig. 8.2, draw an arrow to indicate the energy change that gives rise to this dark line. [1] © UCLES 2014 9702/42/O/N/14 [Turn over
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9 One likely means by which nuclear fusion may be achieved on a practical scale is the D-T reaction.
(a) State what is meant by *nuclear fusion*.
...............................................................................................................................
............................................................................................................................... [1]
(b) In the D-T reaction, a deuterium ( $^2_1$ H) nucleus fuses with a tritium ( $^3_1$ H) nucleus to form a helium-4 ( $^4_2$ He) nucleus. The nuclear equation for the reaction is
$$
^2_1\text{H} + ^3_1\text{H} \rightarrow ^4_2\text{He} + ^1_0\text{n} + \text{energy}
$$
Some data for this reaction are given in Fig. 9.1.
<table>
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<th></th>
<th>mass/u</th>
</tr>
<t21 (iii) Suggest why, for the D-T reaction to take place, the temperature of the deuterium and the tritium must be high. ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... [2] © UCLES 2014 9702/42/O/N/14 [Turn over
22 Section B Answer all the questions in the spaces provided. 10 (a) An ideal operational amplifier (op-amp) has infinite open-loop gain and infinite input resistance (impedance). State three further properties of an ideal op-amp. 1. ............................................................................................................................... ............................................................................................................................ 2. ............................................................................................................................... ............................................................................................................................ 3. .............................................
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The voltmeter has infinite resistance.
The variation with temperature $\theta$ of the resistance $R$ of the thermistor is shown in Fig. 10.2.
Fig. 10.2
(i) When the thermistor is at a temperature of $1.0^\circ\mathrm{C}$ , the voltmeter reads $+1.0\,\mathrm{V}$ .
Show that, for the thermistor at $1.0^\circ\mathrm{C}$ , the potential at A is $-0.20\,\mathrm{V}$ .
[4]
(ii) The potential at A remains at $-0.20\,\mathrm{V}$ .
Determine the voltmeter reading for a thermistor temperature of $15^\circ\mathrm{C}$ .
voltmeter reading = ………………………………………… V 2
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(c) The voltmeter reading for a thermistor temperature of $29^\circ \text{C}$ is $0.35\,\text{V}$ .
(i) Assuming a linear change of voltmeter reading with change of temperature over the range $1^\circ \text{C}$ to $29^\circ \text{C}$ , calculate the voltmeter reading at $15^\circ \text{C}$ .
$$
\text{voltmeter reading} = \underline{\hspace{5cm}}\,\text{V} \quad [1]
$$
(ii) Suggest why your answers in (b)(ii) and (c)(i) are not the same.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ $[1]$
© UCLES 2014
9702/42/O/N/1425 11 The use of X-rays in medical diagnosis gives rise to an increased exposure of the patient to radiation. Explain why (a) an aluminium filter may be placed in the X-ray beam when producing an X-ray image of a patient, ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) the radiation dose received by a patient is differ
26 12 (a) Information may be carried by different channels of communication. State one application, in each case, where information is carried using (i) microwaves, ............................................................................................................................... ............................................................................................................................... [1] (ii) coaxial cables, ............................................................................................................................ ............................................................................................................................... [1] (iii) wire pairs. .....................................................................
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13 A simplified block diagram of a mobile phone handset is shown in Fig. 13.1.
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