科目：物理 Physics (9702)
年份：2016 夏季
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, 19: Capacitance, 20: Magnetic fields, 21: Alternating currents, 23: Nuclear physics, 24: Medical physics
4 Answer all the questions in the spaces provided. 1 A binary star consists of two stars A and B that orbit one another, as illustrated in Fig. 1.1. <div style="text-align: center;">  <br/> Fig. 1.1 </div> The stars are in circular orbits with the centres of both orbits at point P, a distance $d$ from the centre of star A. (a) (i) Explain why the centripetal force acting on both stars has the same magnitude. ............................................................................................................................... ............................................................................................................................... .................................................................................................
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(b) The separation of the centres of the stars is $2.8 \times 10^8$ km.
The mass of star A is $M_A$ . The mass of star B is $M_B$ .
The ratio $\frac{M_A}{M_B}$ is 3.0.
(i) Determine the distance $d$ .
$$
d = \underline{\hspace{5cm}} \text{ km [3]}
$$
(ii) Use your answers in (a)(ii) and (b)(i) to determine the mass $M_B$ of star B.
Explain your working.
$$
M_B = \underline{\hspace{5cm}} \text{ kg [3]}
$$
[Total: 10]
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2 (a) State what is meant by
(i) the Avogadro constant $N_A$ ,
........................................................................................................................... [1]
(ii) the mole.
........................................................................................................................... [2]
(b) A container has a volume of $1.8 \times 10^4 \, \text{cm}^3$ .
The ideal gas in the container has a pressure of $2.0 \times 10^7 \, \text{Pa}$ at a temperature of $17^\circ \text{C}$ .
Show that the amount of gas in the cylinder is 150 mol.
[1]
(c) Gas molecules leak from the container in (b) at a constant rate of $1.5 \times 10^{19} \, \text{s}^{-1}$ .
The temperature remains at $17^\circ \text{C}$ .
In a time $t$ , the amount of gas in the co7
(ii) the time $t$ .
$t = \underline{\hspace{5cm}} \text{s } [3]$
[Total: 9]
3 (a) Explain what is meant by the statement that two bodies are in *thermal equilibrium*.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ [1]
(b) Suggest suitable types of thermometer, one in each case, to measure
(i) the temperature of the flame of a Bunsen burner,
$\underline{\hspace{10cm}}$ [1]
(ii) the change in temperature of a small crystal when it is exposed to a pulse of ultrasound energy.
$\underline{\hspace{10cm}}$ [1]
(c) Some water is heated so that its temperature changes from $26.5^\circ\text{C}$ to a final temperature of $38.0^\circ\text{C}$ .
State, to an appropriate number of decimal places,
(i) the change in temperature in kelvin,
$\text{chang8
4 A metal block hangs vertically from one end of a spring. The other end of the spring is tied to a thread that passes over a pulley and is attached to a vibrator, as shown in Fig. 4.1.
Fig. 4.1
(a) The vibrator is switched off.
The metal block of mass 120g is displaced vertically and then released. The variation with time $t$ of the displacement $y$ of the block from its equilibrium position is shown in Fig. 4.2.
Fig. 4.2
For the vibrations of the block, calculate
(i) the angular frequency $\omega$ ,
$\omega = \underline{\hspace{5cm}} \text{ rad s}^{-1} \text{ [2]}$
© UCLES 2016 9702/42/M/J/169 (ii) the energy of the vibrations. energy = …………………………………………J [2] (b) The vibrator is now switched on. The frequency of vibration is varied from $0.7f$ to $1.3f$ where $f$ is the frequency of vibration of the block in (a). For the block, complete Fig. 4.3 to show the variation with frequency of the amplitude of vibration. Label this line A. [3]  Fig. 4.3 (c) Some light feathers are now attached to the block in (b) to increase air resistance. The frequency of vibration is once again varied from $0.7f$ to $1.3f$. The new amplitude of vibration is measured for each frequency. On Fig. 4.3, draw a line to show the variation with frequency of the amplitude of vibration. Label this line B. 2 © UCLES 2016 9702/42/M/J/16 [Turn over
10
5 The signal from a radio station is amplitude modulated.
(a) State what is meant by *amplitude modulation* (AM).
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) The variation with frequency of the intensity of the signal from the radio station is shown in Fig. 5.1.
<div style="text-align: center;">
<br/>
Fig. 5.1
</div>
State, for this signal,
(i) the bandwidth,
$$
\text{bandwidth} = \underline{\hspace{5c11
(c) A transmission line of length 45 km has an attenuation per unit length of $2.0 \, \text{dB} \, \text{km}^{-1}$ .
The input power to the transmission line is $500 \, \text{mW}$ .
The minimum acceptable signal-to-noise ratio is $24 \, \text{dB}$ for background noise of $5.0 \times 10^{-13} \, \text{W}$ .
(i) Calculate the minimum acceptable power output from the transmission line.
$$
\text{power} = \underline{\hspace{5cm}} \, \text{W} \, [2]
$$
(ii) Use your answer in (i) to determine whether it is possible to transmit the signal along the transmission line.
2
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6 (a) By reference to electric field lines, explain why, for points outside an isolated spherical conductor, the charge on the sphere may be considered to act as a point charge at its centre.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) Two isolated protons are separated in a vacuum by a distance $x$ .
(i) Calculate the ratio
$$
\frac{\text{electric force between the two protons}}{\text{gravitational force between the two protons}}.
$$
ra14
7 (a) State two uses of capacitors in electrical circuits, other than for the smoothing of direct current.
1. ...............................................................................................................................
2. ...............................................................................................................................
[2]
(b) The combined capacitance between terminals A and B of the arrangement shown in Fig. 7.1 is $4.0\ \mu\text{F}$ .
Fig. 7.1
Two capacitors each have capacitance $C$ and the remaining capacitors each have capacitance $3.0\ \mu\text{F}$ .
The potential difference (p.d.) between terminals A and B is $12\ \text{V}$ .
(i) Determine the capacitance $C$ .
$$
C = \underline{\hspace{5cm}}\ \mu\text{F} \ [2]
$$
(ii) Ca15 (iii) Use your answer in (ii) to state the magnitude of the charge on one plate of 1. a capacitor of capacitance $C$ , charge = ………………………………………… $\mu$ C 2. a capacitor of capacitance $3.0\,\mu$ F. charge = ………………………………………… $\mu$ C [2] [Total: 8] © UCLES 2016 9702/42/M/J/16 [Turn over
16 8 An ideal operational amplifier (op-amp) has infinite voltage gain and infinite slew rate. (a) State what is meant by (i) the voltage gain, ........................................................................................................................... [1] (ii) infinite slew rate. ........................................................................................................................... [2] (b) A non-inverting amplifier circuit incorporating an ideal op-amp is shown in Fig. 8.1. Fig. 8.1 The supply to the op-amp is $+9V/-9V$ . The voltage gain of the amplifier circuit is 12. Determine the resistance of resistor R. resistance = ................................................... $\Omega$ [2] © UCLES 2016 9702/42/M/J/16
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(c) For the circuit of Fig. 8.1, the variation with time $t$ of the input potential $V_{IN}$ to the amplifier is shown in Fig. 8.2.
Fig. 8.2
On Fig. 8.3, show the variation with time $t$ of the output potential $V_{OUT}$ for time $t = 0$ to time $t = t_2$.
Fig. 8.3
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9 A magnetic field of flux density $B$ is normal to face PQRS of a slice of a conducting material, as shown in Fig. 9.1.
<div style="text-align: center;">
<br/>
Fig. 9.1
</div>
A current $I$ in the slice is normal to face QRZY of the slice.
The Hall voltage $V_H$ across the slice is given by the expression
$$
V_H = \frac{BI}{ntq}.
$$
(a) (i) State what is represented by the symbol $n$ .
............................................................................................................................ [1]
(ii) The symbol $t$ represents the length of one side of the slice. Use letters from Fig. 9.1 to identify $t$ .
............................................................................................................................ [1]
19 (ii) In some semiconducting materials, electrons are mainly responsible for conduction. In other semiconducting materials, holes are mainly responsible for conduction. Suggest and explain the difference, if any, that conduction by electrons or by holes will have on the Hall voltage. ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... 3 © UCLES 2016
20 10 Two coils P and Q are placed close to one another, as shown in Fig. 10.1. <div style="display: flex; justify-content: space-between; width: 100%;"> <div style="text-align: center;"> coil P<br>  </div> <div style="text-align: center;"> coil Q<br>  </div> </div> Fig. 10.1 (a) The current in coil P is constant. An iron rod is inserted into coil P. Explain why, during the time that the rod is moving, there is a reading on the voltmeter connected to coil Q. ............................................................................................................................... ............................................................................................................................... ...........................
21 (b) The current in coil P is now varied as shown in Fig. 10.2.  Fig. 10.2 On Fig. 10.3, show the variation with time of the reading of the voltmeter connected to coil Q for time $t = 0$ to time $t = t_2$.  Fig. 10.3 4 © UCLES 2016 9702/42/M/J/16 [Turn over
22 11 A bridge rectifier contains four ideal diodes A, B, C and D, as shown in Fig. 11.1. Fig. 11.1 The output of the rectifier is connected to a load L of resistance 2.4 kΩ. (a) On Fig. 11.1, mark with the letter P the positive terminal of the load. [1] (b) The variation with time $t$ of the potential difference $V$ across the input to the rectifier is shown in Fig. 11.2. Fig. 11.2 Calculate the root-mean-square (r.m.s.) current in the load L. r.m.s. current = __________________________ A [2] © UCLES 2016 9702/42/M/J/16 Note: The image contains a circuit diagram (Fig. 11.1) and a graph (Fig. 11.2), which are described in the text but cannot be rendered as actual images in Markdown. The text descriptions and equations are preserved as requested. The graph is described as a plot o
23 (c) The potential difference across the load L is to be smoothed using a capacitor. (i) On Fig. 11.1, draw the symbol for a capacitor, connected to produce smoothing. [1] (ii) The minimum potential difference across the load L with the smoothing capacitor connected is 3.0 V. On Fig. 11.2, sketch the variation with time $t$ of the potential difference across the load L. 3 © UCLES 2016 9702/42/M/J/16 [Turn over
24 12 High-energy electrons collide with a metal target, producing X-ray photons. The variation with wavelength of the intensity of the X-ray beam is illustrated in Fig. 12.1.  Fig. 12.1 (a) Explain why there is (i) a continuous distribution of wavelengths, ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...............................................................................................................................
25 (ii) Suggest the reason for this filtering. .................................................................................................................... [1] .................................................................................................................... [Total: 8] © UCLES 2016 9702/42/M/J/16 [Turn over
26 13 (a) Explain what is meant by gamma radiation ( $\gamma$ -radiation). ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A source of gamma radiation is placed a fixed distance away from a detector and counter, as illustrated in Fig. 13.1. <div style="text-align: center;">  </div> Fig. 13.1 A sheet of lead of thickness $x$ is placed between the source and the detector. The average count rate $C$ , corrected for backgro
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$\ln(C/s^{-1})$
4.00
3.75
3.50
3.25
3.00
2.75
0 2 4 6 8 10 12 14 16
$x/mm$
Fig. 13.2
The absorption of gamma radiation in lead may be represented by the equation
$$
C = C_0 e^{-\mu x}
$$
where $C_0$ is the count rate for $x = 0$ and $\mu$ is the linear attenuation (absorption) coefficient.
Use Fig. 13.2 to determine the linear attenuation coefficient $\mu$ for this gamma radiation in lead.
$\mu = \underline{\hspace{5cm}} \text{ mm}^{-1} \text{ [4]}$
Question 13 continues on the next page.
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