科目：物理 Physics (9702)
年份：2021 夏季
试卷：Paper 43
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, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
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Answer all the questions in the spaces provided.
1 The Earth may be assumed to be an isolated uniform sphere with its mass of $6.0 \times 10^{24}$ kg concentrated at its centre.
A satellite of mass 1200 kg is in a circular orbit about the Earth in the Earth’s gravitational field. The period of the orbit is 94 minutes.
(a) Define gravitational field strength.
............................................................................................................................ [1]
(b) Calculate the radius of the orbit of the satellite.
radius = ................................................... m [3]
(c) Rockets on the satellite are fired so that the satellite enters a different circular orbit that has a period of 150 minutes. The change in the mass of the satellite may be a5 (iii) Determine the magnitude of the change in the gravitational potential energy of the satellite. change in potential energy = ........................................... J 3 © UCLES 2021 9702/43/M/J/21 [Turn over
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2 An ideal gas is contained in a cylinder by means of a movable frictionless piston, as illustrated in Fig. 2.1.
<div style="text-align: center;">
</div>
Fig. 2.1
Initially, the gas has a volume of $1.8 \times 10^{-3} \, \text{m}^3$ at a pressure of $3.3 \times 10^5 \, \text{Pa}$ and a temperature of $310 \, \text{K}$ .
(a) Show that the number of gas molecules in the cylinder is $1.4 \times 10^{23}$ .
[2]
(b) Use kinetic theory to explain why, when the piston is moved so that the gas expands, this causes a decrease in the temperature of the gas.
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(c) The gas expands so that its volume increases to $2.4 \times 10^{-3} \, \text{m}^3$ at a pressure of $2.3 \times 10^5 \, \text{Pa}$ and a temperature of $288 \, \text{K}$ , as shown in Fig. 2.2.
<table>
<tr>
<td> $1.8 \times 10^{-3} \, \text{m}^3$ <br> $3.3 \times 10^5 \, \text{Pa}$ <br> $310 \, \text{K}$ </td>
<td> $\longrightarrow$ </td>
<td> $2.4 \times 10^{-3} \, \text{m}^3$ <br> $2.3 \times 10^5 \, \text{Pa}$ <br> $288 \, \text{K}$ </td>
</tr>
</table>
Fig. 2.2
(i) The average translational kinetic energy $E_K$ of a molecule of an ideal gas is given by
$$
E_K = \frac{3}{2} kT
$$
where $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature.
Calculate the increase in internal energy $\Delta U$ of the gas during the expansion.
$\Delta U = \und8
3 (a) State what is meant by simple harmonic motion.
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............................................................................................................................... [2]
(b) A trolley of mass $m$ is held on a horizontal surface by means of two springs. One spring is attached to a fixed point P. The other spring is connected to an oscillator, as shown in Fig. 3.1.
<div style="text-align: center;">
</div>
Fig. 3.1
The springs, each having spring constant $k$ of $130\,\text{N}\,\text{m}^{-1}9 (c) The oscillator in (b) is switched on. The frequency of oscillation of the oscillator is varied, keeping its amplitude of oscillation constant. The amplitude of oscillation of the trolley is seen to vary. The amplitude is a maximum at the frequency calculated in (b). (i) State the name of the effect giving rise to this maximum. ................................................................................................................... [1] (ii) At any given frequency, the amplitude of oscillation of the trolley is constant. Explain how this indicates that there are resistive forces opposing the motion of the trolley. ................................................................................................................... ........................................
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11 4 Outline the use of ultrasound to obtain diagnostic information about internal body structures. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... .....................................................
12 5 (a) State what is meant by the *amplitude modulation (AM)* of a radio wave. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A radio wave is modulated by an audio signal. The variation with frequency $f$ of the amplitude of the modulated wave is shown in Fig. 5.1.  Fig. 5.1 Determine: (i) the wavelength of the carrier wave wavelength = ........................................... m [1] (ii) the bandwidth of the modul
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(c) The power of a radio signal at a transmitter is $P_T$ .
At a receiver, the received power $P_R$ is given by the expression
$$
P_R = \frac{0.082 P_T}{x^2}
$$
where $x$ is the distance, in metres, between the transmitter and the receiver.
For the transmission of this signal, the attenuation is 73 dB.
Determine the distance $x$ .
$x = \underline{\hspace{5cm}} \text{ m [3]}$
[Total: 8]
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6 (a) An isolated metal sphere of radius $r$ is charged so that the electric field strength at its surface is $E_0$ .
On Fig. 6.1, sketch the variation of the electric field strength $E$ with distance $x$ from the centre of the sphere. Your sketch should extend from $x = 0$ to $x = 3r$ .
<div style="text-align: center;">
<br/>
Fig. 6.1
<br/>
[3]
</div>
(b) The de Broglie wavelength of a particle is $\lambda_0$ when its momentum is $p_0$ .
On Fig. 6.2, sketch the variation with momentum $p$ of the de Broglie wavelength $\lambda$ of the particle for values of momentum from $\frac{p_0}{2}$ to $p_0$ .
<div style="text-align: center;">
<br/>
Fig. 6.2
<br/>
[2]
</div>
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Note: The images reference15 (c) A radioactive isotope decays with a half-life of 15 s to form a stable product. A fresh sample of the radioactive isotope at time $t = 0$ contains $N_0$ nuclei and no nuclei of the stable product. On Fig. 6.3, sketch the variation with $t$ of the number $n$ of nuclei of the stable product for time $t = 0$ to time $t = 45$ s. <div style="text-align: center;">  <br/> Fig. 6.3 </div> 3 © UCLES 2021 9702/43/M/J/21 [Turn over
16 7 (a) State what is meant by the *capacitance* of a parallel plate capacitor. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A capacitor of capacitance $C$ is connected into the circuit shown in Fig. 7.1. <div style="text-align: center;">  <br/> Fig. 7.1 </div> When the two-way switch is in position A, the capacitor is charged so that the potential difference across it is $V$ . The switch moves to position B and
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(ii) For a potential difference $V$ of $150\,\text{V}$ and a frequency $f$ of $60\,\text{Hz}$ , the average current in the ammeter is $4.8\,\mu\text{A}$ .
Calculate the capacitance, in pF, of the capacitor.
capacitance = ………………………………………… pF [2]
(c) A second capacitor, having the same capacitance as the capacitor in (b), is connected into the circuit of Fig. 7.1. The two capacitors are connected in series.
State and explain the new reading on the ammeter.
new reading = ………………………………………… $\mu\text{A}$
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
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© UCLES 2021 9702/43/M/J/21 [Turn over18 8 The variation with temperature of the resistance of a thermistor is shown in Fig. 8.1.  Fig. 8.1 A student includes the thermistor and an ideal operational amplifier (op-amp) in the circuit of Fig. 8.2.  Fig. 8.2 © UCLES 2021 9702/43/M/J/21
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(a) Calculate the potential $V^+$ at the non-inverting input of the op-amp.
$$
V^+ = \underline{\hspace{5cm}} \text{ V [2]}
$$
(b) At $10^\circ \text{C}$ , the resistance of the thermistor is $2.5 \text{k}\Omega$ .
State and explain whether the light-emitting diode (LED) is emitting light.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ [2]
(c) Explain why the student’s circuit will not indicate any change in temperature above $0^\circ \text{C}$ .
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ [2]
(d) The resistor of resistance $5.0 \text{k}\Omega$ is changed to a resistor of resistance $R$ so that the LED switches on or off at a temperature of $20^\circ \text{C}$ .
Determine $R$ in $\text{k}\Omega$ .
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9 (a) State what is meant by a magnetic field.
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(b) A rectangular piece of aluminium foil is situated in a uniform magnetic field of flux density $B$ , as shown in Fig. 9.1.
<div style="text-align: center;">
</div>
Fig. 9.1
The magnetic field is normal to the face PQRS of the foil.
Electrons, each of charge $-q$ , enter the foil at right angles to the face PQTV.
(i) On Fi21
(c) The Hall voltage $V_H$ developed across the foil in (b) is given by the expression
$$
V_H = \frac{BI}{ntq}
$$
where $I$ is the current in the foil.
(i) State the meaning of the quantity $n$ .
........................................................................................................................... [1]
(ii) Using the letters on Fig. 9.1, identify the distance $t$ .
........................................................................................................................... [1]
(d) Suggest why, in practice, Hall probes are usually made using a semiconductor material rather than a metal.
........................................................................................................................... [1]
[Total: 9]
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10 (a) State Lenz’s law.
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............................................................................................................................... [2]
(b) A metal ring is suspended from a fixed point P by means of a thread, as shown in Fig. 10.1.
<div style="display: flex; justify-content: space-between;">
<div style="text-align: center;">
<br/>
Fig. 10.1
</div>
<div style="text-align: center;">
<br/>
Fig. 10.2
</div>
</div>
The ring is displaced a dist23 (c) The ring in (b) is now cut so that it has the shape shown in Fig. 10.3. Fig. 10.3 Explain why, when the procedure in (b) is repeated, the cut ring completes more oscillations than the complete ring when oscillating between the poles of the magnet. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... 3 © UCLES 2021 9702/43/M/
24 11 (a) State how, in a modern X-ray tube, the intensity of the X-ray beam and its hardness are controlled. intensity: ....................................................................................................................... ....................................................................................................................... hardness: ....................................................................................................................... ....................................................................................................................... [2] (b) A model of a limb consists of soft tissue and bone, as illustrated in Fig. 11.1.  Fig. 11.1 The soft tissue has a thickness of 9.0 cm. The bone within
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A parallel beam of X-rays of intensity $I_0$ is incident normally on the model.
Calculate, in terms of $I_0$:
(i) the transmitted intensity $I_S$ through soft tissue alone
$$
I_S = \underline{\hspace{5cm}} \quad I_0 \ [2]
$$
(ii) the transmitted intensity $I_C$ through soft tissue and bone.
$$
I_C = \underline{\hspace{5cm}} \quad I_0 \ [2]
$$
(c) By reference to your answers in (b), suggest, with a reason, whether good contrast on an X-ray image would be obtained.
$\underline{\hspace{10cm}}$ [1]
[Total: 7]
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27 12 (a) Electromagnetic radiation of a single constant frequency is incident on a metal surface. This causes an electron to be emitted. Explain why the maximum kinetic energy of the electron is independent of the intensity of the incident radiation. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) Ultraviolet radiation