科目：物理 Physics (9702)
年份：2021 冬季
试卷：Paper 43
总页数：24
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 19: Capacitance, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
4 Answer all the questions in the spaces provided. 1 (a) With reference to velocity and acceleration, describe uniform circular motion. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Two cars are moving around a horizontal circular track. One car follows path X and the other follows path Y, as shown in Fig. 1.1. start and finish line track path X 27 m 318 m path Y Fig. 1.1 (not to scale) The radius of path X is 318 m. Path Y is parallel
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(ii) Both cars move around the track. Each car has the maximum speed at which it can move without sliding.
Complete Table 1.1, by placing one tick in each row, to indicate how the quantities indicated for the car on path Y compare with the car on path X.
**Table 1.1**
<table>
<tr>
<th></th>
<th>Y less than X</th>
<th>Y same as X</th>
<th>Y greater than X</th>
</tr>
<tr>
<td>centripetal acceleration</td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>maximum speed</td>
<td></td>
<td></td>
<td></td>
</tr>
<tr>
<td>time taken for one lap of the track</td>
<td></td>
<td></td>
<td></td>
</tr>
</table>
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2 (a) Define gravitational potential.
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............................................................................................................................... [2]
(b) The Earth E and the Moon M can both be considered as isolated point masses at their centres. The mass of the Earth is $5.98 \times 10^{24}$ kg and the mass of the Moon is $7.35 \times 10^{22}$ kg. The Earth and the Moon are separated by a distance of $3.84 \times 10^8$ m, as shown in Fig. 2.1.
<div style="text-align: center;">
</div>
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(iii) Calculate the gravitational potential $\phi$ at point P.
$\phi = \underline{\hspace{5cm}} \text{ J kg}^{-1} [3]$
[Total: 9]
© UCLES 2021 9702/43/O/N/21 [Turn over8 3 (a) Define specific heat capacity. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A sealed container of fixed volume $V$ contains $N$ molecules, each of mass $m$ , of an ideal gas at pressure $p$ . (i) State an expression, in terms of $V$ , $N$ , $p$ and the Boltzmann constant $k$ , for the thermodynamic temperature $T$ of the gas. ..............................................................................................................
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(ii) Use the expression in (b)(ii) and the information in (c)(i) to show that the specific heat capacity $c$ of the gas is given by
$$
c = \frac{3k}{2m}.
$$
[2]
(d) The container in (b) is now replaced with one that does not have a fixed volume. Instead, the gas is able to expand, so that the pressure of the gas remains constant as thermal energy is supplied.
Suggest, with a reason, how the specific heat capacity of the gas would now compare with the value in (c)(ii).
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4 A trolley on a track is attached by springs to fixed blocks X and Y, as shown in Fig. 4.1. The track contains many small holes through which air is blown vertically upwards. This results in the trolley resting on a cushion of air rather than being in direct contact with the track.
<div style="text-align: center;">
</div>
Fig. 4.1
The trolley is pulled to one side of its equilibrium position and then released so that it oscillates initially with simple harmonic motion. After a short time, the air blower is switched off. The variation with time $t$ of the distance $L$ of the trolley from block X is shown in Fig. 4.2.
<div style="text-align: center;">
</div>
Fig. 4.2
(a) Use Fig. 4.2 to determine:
(i) the initial amplitude of th11
(ii) the angular frequency $\omega$ of the oscillations
$\omega = \underline{\hspace{5cm}} \text{ rad s}^{-1} \ [2]$
(iii) the maximum speed $v_0$ , in cm s $^{-1}$ , of the oscillating trolley.
$v_0 = \underline{\hspace{5cm}} \text{ cm s}^{-1} \ [2]$
(b) Apart from the quantities in (a), describe what may be deduced from Fig. 4.2 about the motion of the trolley between time $t = 0$ and time $t = 24$ s. No calculations are required.
$\underline{\hspace{15cm}}$
$\underline{\hspace{15cm}}$
$\underline{\hspace{15cm}}$
$\underline{\hspace{15cm}}$
$\underline{\hspace{15cm}} \ [3]$
(c) On Fig. 4.3, sketch the variation with $L$ of the velocity $v$ of the trolley for its first complete oscillation.
Fig. 4.3
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5 An analogue signal is to be transmitted to a receiver. Before transmission, the signal passes through an analogue-to-digital converter (ADC). After transmission it passes through a digital-to-analogue converter (DAC) before finally reaching the receiver, as shown in Fig. 5.1.
plaintext
input signal ──┐
│ ADC
└─── transmission line ──── DAC ── receiver
```
Fig. 5.1
(a) State two advantages of converting the signal into digital form for transmission.
1. ...............................................................................................................
............................................................................................................
2. ..............................................................................14 (ii) Part of the signal received by the receiver, after the sampled signal has passed through the DAC, is shown in Fig. 5.3.  Fig. 5.3 On Fig. 5.3, complete the line to show the received signal for time 0 to time 12 ms. [2] © UCLES 2021 9702/43/O/N/21
15 (c) The ADC in (b) is replaced with one that has a sampling frequency of 500 Hz and uses 3-bit sampling, with the least significant bit corresponding to 2 mV. On Fig. 5.4, sketch the signal that is now received, after passing through the DAC, from time 0 to time 12 ms.  Fig. 5.4 3 © UCLES 2021 9702/43/O/N/21 [Turn over
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6 (a) A capacitor consists of two parallel metal plates, separated by air, at a variable distance $x$ apart, as shown in Fig. 6.1. The capacitance $C$ is inversely proportional to $x$ .
<div style="text-align: center;">
</div>
Fig. 6.1
The capacitor is charged by a supply so that there is a potential difference (p.d.) $V$ between the plates.
State expressions, in terms of $C$ and $V$ , for the charge $Q$ on one of the plates and for the energy $E$ stored in the capacitor.
$$
Q = \text{........................................} \quad E = \text{........................................} \quad [1]
$$
(b) The charged capacitor in (a) is now disconnected from the supply. The plates of the capacitor are initially separated by distance $L$ . They are then moved c17
(ii) the new charge $Q_N$ on one of the plates
$$
Q_N = \text{..................................................} [1]
$$
(iii) the new p.d. $V_N$ between the plates.
$$
V_N = \text{..................................................} [1]
$$
(c) Explain whether reducing the separation of the plates in (b) results in an increase or decrease in the energy stored in the capacitor.
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© UCLES 2021 9702/43/O/N/21 [Turn over18 7 (a) State two properties of an ideal operational amplifier (op-amp). 1. ............................................................................................................................... 2. ............................................................................................................................... [2] (b) Fig. 7.1 shows a circuit that includes an ideal op-amp and two identical resistors R. Fig. 7.1 State the names of components X and Y. X: ........................................... Y: ........................................... [1] (c) (i) Explain why the op-amp in Fig. 7.1 has only two possible output states. ............................................................................................................................... .....
19 (iii) Describe the environmental condition under which the lamp L in Fig. 7.1 will light. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (iv) Suggest the purpose of the variable resistor V in the circuit. ............................................................................................................................... ....................................................................................................................
20 8 (a) Define the tesla. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A stiff metal wire is used to form a rectangular frame measuring 8.0 cm × 6.0 cm. The frame is open at the top, and is suspended from a sensitive newton meter, as shown in Fig. 8.1.  Fig. 8.1 The open ends of the frame are connected to a power supply so that there is a current of 5.0A in the frame in the direction indicated in Fig. 8.1. The frame is
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(i) Determine the magnetic flux density $B$, in mT.
$B = \underline{\hspace{5cm}} \text{ mT [2]}$
(ii) State, with a reason, whether the change in the reading on the newton meter is an increase or a decrease.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ [1]
(iii) The frame is lowered further so that the vertical sides start to enter the magnetic field. Suggest what effect this will have on the frame.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ 1
© UCLES 2021 9702/43/O/N/21 [Turn over22 9 (a) State, by reference to the power dissipated in a resistor, what is meant by the root-mean-square (r.m.s.) value of an alternating voltage. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) A coil is rotating freely, on frictionless bearings, at constant speed in a uniform magnetic field. This rotation causes an in
23 (c) State and explain the effect on the motion of the coil in (b) of connecting a load resistor across its terminals. ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... 2 © UCLES 2021 9702/43/O/N/21 [Turn over
24 10 (a) State an experimental phenomenon that provides evidence for: (i) the particulate nature of electromagnetic radiation ................................................................................................................... [1] (ii) the wave nature of matter. ................................................................................................................... [1] (b) A particle of matter moves with momentum $p$ . (i) State the equation that gives the effective wavelength $\lambda$ of the particle. State the name of any other symbols used. [2] (ii) State the name given to the wavelength of the moving particle. ................................................................................................................... [1] (c) Electrons ar
25 11 (a) State, for an X-ray image, what is meant by: (i) sharpness ............................................................................................................................... ............................................................................................................................... [1] (ii) contrast. ............................................................................................................................... ............................................................................................................................... [1] (b) A parallel X-ray beam passes through a thickness of 2.3 cm of soft body tissue. The intensity of the emerging beam is 12% of the intensity of the incident beam. Calculate the linear a
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12 (a) Define radioactive decay constant.
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............................................................................................................................... [2]
(b) A sample of radioactive iodine-131 ( $^{131}_{53}\text{I}$ ) of mass $5.87 \times 10^{-10} \, \text{kg}$ has an activity of $2.92 \times 10^9 \, \text{Bq}$ .
Determine the decay constant of iodine-131.
decay constant = ................................................... s⁻¹ [3]
(c) Suggest two reasons why a detector placed near to the sample in (b) woul27 BLANK PAGE © UCLES 2021 9702/43/O/N/21