科目：物理 Physics (9702)
年份：2021 春季
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 questions in the spaces provided. 1 (a) State Newton’s law of gravitation. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) Planets have been observed orbiting a star in another solar system. Measurements are made of the orbital radius $r$ and the time period $T$ of each of these planets. The variation with $R^3$ of $T^2$ is shown in Fig. 1.1.  Fig. 1.1 © UCLES 2021 9702/42/F/M/21
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The relationship between $T$ and $R$ is given by
$$
T^2 = \frac{4\pi^2 R^3}{GM}
$$
where $G$ is the gravitational constant and $M$ is the mass of the star.
Determine the mass $M$ .
$M = \underline{\hspace{5cm}} \text{ kg [3]}$
(c) A rock of mass $m$ is also in orbit around the star in (b). The radius of the orbit is $r$ .
(i) Explain why the gravitational potential energy of the rock is negative.
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$
$\underline{\hspace{10cm}}$ [3]
(ii) Show that the kinetic energy $E_k$ of the rock is given by
$$
E_k = \frac{GMm}{2r}.
$$
[2]
(iii) Use the expression in (c)(ii) to derive an expression for the total energy of the rock.
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2 A fixed mass of an ideal gas is at a temperature of $21^\circ \text{C}$ . The pressure of the gas is $2.3 \times 10^5 \text{ Pa}$ and its volume is $3.5 \times 10^{-3} \text{ m}^3$ .
(a) (i) Calculate the number $N$ of molecules in the gas.
$$
N = \text{..................................................} \quad [2]
$$
(ii) The mass of one molecule of the gas is $40 \, \text{u}$ .
Determine the root-mean-square (r.m.s.) speed of the gas molecules.
$$
\text{r.m.s. speed} = \text{..................................................} \quad \text{m s}^{-1} \quad [2]
$$
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(b) The temperature of the gas is increased by $84^\circ \text{C}$ .
Calculate the value of the ratio
$$
\frac{\text{new r.m.s. speed of molecules}}{\text{original r.m.s. speed of molecules}}
$$
ratio = ………………………………………… 2
© UCLES 2021 9702/42/F/M/21 [Turn over8 3 (a) Using a simple kinetic model of matter, describe the structure of a solid. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) The specific latent heat of vaporisation is much greater than the specific latent heat of fusion for the same substance. Explain this, in terms of the spacing of molecules. ............................................................................................................................... .................
9 (i) Determine the temperature at which the substance melts. temperature = ………………………………………… °C [1] (ii) The power of the heater is 150 W. Use data from Fig. 3.1 to calculate, in kJ kg⁻¹, the specific latent heat of vaporisation $L$ of the substance. $L$ = ………………………………………… kJ kg⁻¹ [3] (iii) Suggest what can be deduced from the fact that section Q on the graph is less steep than section P. ……………………………………………………………………………………………………… [1] ……………………………………………………………………………………………………… [Total: 8] © UCLES 2021 9702/42/F/M/21 [Turn over
10 4 (a) The defining equation of simple harmonic motion is $$ a = -\omega^2 x. $$ State the significance of the minus (–) sign in the equation. ............................................................................................................................ [1] (b) A trolley rests on a bench. Two identical stretched springs are attached to the trolley as shown in Fig. 4.1. The other end of each spring is attached to a fixed support.  Fig. 4.1 The unstretched length of each spring is 12.0 cm. The spring constant of each spring is 8.0 N m⁻¹. When the trolley is in equilibrium the length of each spring is 18.0 cm. The trolley is displaced 4.8 cm to one side and then released. Assume that resistive forces on the trolley are negligible. (i) Show that t
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(ii) The mass of the trolley is 250 g.
Calculate the maximum acceleration $a$ of the trolley.
$$
a = \underline{\hspace{5cm}} \text{ m s}^{-2} \text{ [1]}
$$
(iii) Use your answer in (ii) to determine the period $T$ of the subsequent oscillation.
$$
T = \underline{\hspace{5cm}} \text{ s [3]}
$$
(iv) The experiment is repeated with an initial displacement of the trolley of 2.4 cm.
State and explain the effect, if any, this change has on the period of the oscillation of the trolley.
...............................................................................................................................
...............................................................................................................................
.............................................12 5 (a) (i) State what is meant by the *amplitude modulation (AM)* of a radio wave. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) State two advantages of AM transmissions when compared with frequency modulation (FM) transmissions. 1. ............................................................................................................................... ...................................................................................
13 (c) Another audio signal with the same maximum frequency is transmitted using a different carrier wave frequency. The lowest frequency of this modulated wave is equal to the highest frequency of the modulated wave in (b). Determine the frequency of this carrier wave. frequency = ……………………………………… kHz 1 © UCLES 2021 9702/42/F/M/21 [Turn over
14 6 (a) State a similarity between the gravitational field lines around a point mass and the electric field lines around a point charge. ........................................................................................................................... [1] (b) The variation with radius $r$ of the electric field strength $E$ due to an isolated charged sphere in a vacuum is shown in Fig. 6.1.  Fig. 6.1 Use data from Fig. 6.1 to: (i) state the radius of the sphere radius = ................................................ cm [1] © UCLES 2021 9702/42/F/M/21
15 (ii) calculate the charge on the sphere. charge = ………………………………………… C [2] (c) Using the formula for the electric potential due to an isolated point charge, determine the capacitance of the sphere in (b). capacitance = ………………………………………… F 3 © UCLES 2021 9702/42/F/M/21 [Turn over
16 7 (a) Fig. 7.1 shows the circuit diagram containing an operational amplifier (op-amp). Fig. 7.1 (i) State the name of this type of amplifier. ................................................................................................................... [1] (ii) Show that the gain of the amplifier is 6.0. [1] © UCLES 2021 9702/42/F/M/21
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(iii) At time $t = 0$ the input potential $V_{IN}$ is zero. $V_{IN}$ then gradually increases with time $t$ as shown in Fig. 7.2.
Fig. 7.2
On Fig. 7.2 sketch a line to show the variation with time $t$ of the output potential $V_{OUT}$ from time $t = 0$ to time $t = T$.
[2]
(iv) State how the circuit of Fig. 7.1 may be changed so that the gain of the amplifier is dependent on light intensity.
...............................................................................................................................
...............................................................................................................................
[1]
(b) An op-amp is to be used to switch on a high-voltage heater.
(i) State the name of the component used as t18 8 (a) Two long straight wires P and Q are parallel to each other, as shown in Fig. 8.1. There is a current in each wire in the direction shown. The pattern of the magnetic field lines in a plane normal to wire P due to the current in the wire is also shown. <div style="display: flex; justify-content: space-between; width: 100%;"> <div style="text-align: center;"> wire P<br> plane<br> magnetic field pattern </div> <div style="text-align: center;"> wire Q<br> direction of current </div> </div> Fig. 8.1 (i) Draw arrows on the magnetic field lines in Fig. 8.1 around wire P to show the direction of the field. [1] (ii) Determine the direction of the force on wire Q due to the magnetic field from wire P. [1] (iii) The current in wire Q is less than the current in wire P. State and e
19 (b) Nuclear magnetic resonance imaging (NMRI) is used to obtain diagnostic information about internal structures in the human body. Radio waves are produced and directed towards the body. The radio waves affect the protons within the body. (i) Explain why radio waves are used. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) Explain why the radio waves are applied in pulses. ...................................................................
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9 (a) Define magnetic flux linkage.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) A solenoid of diameter 6.0 cm and 540 turns is placed in a uniform magnetic field as shown in Fig. 9.1.
Fig. 9.1
The variation with time $t$ of the magnetic flux density is shown in Fig. 9.2.
Fig. 9.2
Calculate the maximum magnitude of the induced electromotive force (e.m.f.) in the solenoid.
$$
\text{e.m.f.} = 21 (c) A thin copper sheet X is supported on a rigid rod so that it hangs between the poles of a magnet as shown in Fig. 9.3.  Fig. 9.3 Sheet X is displaced to one side and then released so that it oscillates. A motion sensor is used to record the displacement of X. A second thin copper sheet Y replaces sheet X. Sheet Y has the same overall dimensions as X but is cut into the shape shown in Fig. 9.4.  Fig. 9.4 The motion sensor is again used to record the displacement. The graph in Fig. 9.5 shows the variation with time $t$ of the displacement $s$ of each copper sheet.  Fig. 9.5 © UCLES 2021 9702/42/F/M/21 [Turn over
22 (i) State the name of the phenomenon illustrated by the gradual reduction in the amplitude of the dashed line. ................................................................................................................... [1] (ii) Deduce which copper sheet is represented by the dashed line. Explain your answer using the principles of electromagnetic induction. ................................................................................................................... ................................................................................................................... ................................................................................................................... ..........................................................................
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10 The output potential difference (p.d.) of an alternating power supply is represented by
$$
V = 320 \sin(100 \pi t)
$$
where $V$ is the p.d. in volts and $t$ is the time in seconds.
(a) Determine the root-mean-square (r.m.s.) p.d. of the power supply.
$$
\text{r.m.s. p.d.} = \underline{\hspace{5cm}} \text{ V [1]}
$$
(b) Determine the period $T$ of the output.
$$
T = \underline{\hspace{5cm}} \text{ s [2]}
$$
(c) The power supply is connected to resistor $R$ and a diode in the circuit shown in Fig. 10.1.
<div style="text-align: center;">
<br/>
Fig. 10.1
</div>
(i) State the name of the type of rectification produced by the diode in Fig. 10.1.
$\underline{\hspace{10cm}}$ [1]
© UCLES 2021 9702/42/F/M/21 [Turn over24 (ii) On Fig. 10.2 sketch the variation with time $t$ of the p.d. $V_R$ across R from time $t = 0$ to time $t = 40$ ms.  Fig. 10.2 [3] (iii) On Fig. 10.1, draw the symbol for a component that may be connected to produce smoothing of $V_R$. 1 © UCLES 2021 9702/42/F/M/21
25 11 (a) Electrons are accelerated through a potential difference of 15 kV. The electrons collide with a metal target and a spectrum of X-rays is produced. (i) Explain why a continuous spectrum of energies of X-ray photons is produced. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (ii) Calculate the wavelength of the hig
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(b) A beam of X-rays has an initial intensity $I_o$ . The beam is directed into some body tissue. After passing through a thickness $x$ of tissue the intensity is $I$ . The graph in Fig. 11.1 shows the variation with $x$ of $\ln(I/I_o)$ .
<div style="text-align: center;">
</div>
Fig. 11.1
(i) Determine the linear attenuation (absorption) coefficient $\mu$ for this beam of X-rays in the tissue.
$$
\mu = \underline{\hspace{5cm}} \text{ cm}^{-1} \text{ [2]}
$$
(ii) Determine the thickness of tissue that the X-ray beam must pass through so that the intensity of the beam is reduced to 5.0% of its initial value.
$$
\text{thickness} = \underline{\hspace{5cm}} \text{ cm [2]}
$$
[Total: 10]
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12 (a) Radioactive decay is both spontaneous and random.
State what is meant by:
1. spontaneous decay ……………………………………………………………………………………
…………………………………………………………………………………………………………
2. random decay ………………………………………………………………………………………
………………………………………………………………………………………………………… [2]
(b) Strontium-90 ( $^{90}_{38}\text{Sr}$ ) is an unstable nuclide.
The activity of a sample of $1.0 \times 10^{-9}$ kg of strontium-90 is 5.2 MBq.
(i) Determine the decay constant $\lambda$ of strontium-90.
$\lambda = \underline{\hspace{5cm}} \text{ s}^{-1} \text{ [3]}$
(ii) The activity of the sample after a time of 1.0 half lives is found to be greater than the expected 2.6 MBq.
Suggest a possible reason for this.
………………………………………………………………………………………………………………… [1]
[Total: 6]
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