科目：物理 Physics (9702)
年份：2021 冬季
试卷：Paper 42
总页数：20
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, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
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Answer all the questions in the spaces provided.
1 (a) State what is meant by centripetal acceleration.
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(b) An unpowered toy car moves freely along a smooth track that is initially horizontal. The track contains a vertical circular loop around which the car travels, as shown in Fig. 1.1.
<div style="text-align: center;">
</div>
Fig. 1.1
The mass of the car is 230 g and the5
(c) The initial speed at which the car in (b) moves along the track is $3.8 \, \text{m} \, \text{s}^{-1}$ .
Determine whether the car is in contact with the track at point Y. Show your working.
[3]
(d) Suggest, with a reason but without calculation, whether your conclusion in (c) would be different for a car of mass 460 g moving with the same initial speed.
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2 (a) State the relationship between gravitational potential and gravitational field strength.
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(b) A moon of mass $M$ and radius $R$ orbits a planet of mass $3M$ and radius $2R$ . At a particular time, the distance between their centres is $D$ , as shown in Fig. 2.1.
<div style="text-align: center;">
</div>
Fig. 2.1
Point P is a point along the line between the centres of t7 (i) Explain why $\phi$ is negative throughout the entire range $x = 2R$ to $x = D - R$ . ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (ii) One of the features of Fig. 2.2 is that $\phi$ is negative throughout. Describe **two** other features of Fig. 2.2. 1. .............................................................
8 3 (a) One of the assumptions of the kinetic theory of gases is that all collisions involving molecules of the gas are elastic. (i) State what is meant by an *elastic collision*. ............................................................................................................................... ............................................................................................................................... [1] (ii) State two other assumptions of the kinetic theory of gases. 1. ............................................................................................................................... ............................................................................................................................... 2. .........................
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(iii) the average force exerted by the molecule on the shaded face
$$
\text{force} = \quad \text{[1]}
$$
(iv) the pressure on the shaded face if the force in (iii) is exerted over the whole area of the face.
$$
\text{pressure} = \quad \text{[1]}
$$
(c) When the model described in (b) is extended to three dimensions, and to a gas containing $N$ molecules, each of mass $m$ , travelling with mean-square speed $\langle c^2 \rangle$ , it can be shown that
$$
pV = \frac{1}{3}Nm\langle c^2 \rangle
$$
where $p$ is the pressure exerted by the gas and $V$ is the volume of the gas.
Use this expression, together with the equation of state of an ideal gas, to show that the average translational kinetic energy $E_K$ of a molecule of an ideal gas is given by
$$
E_K = \frac{3}{2}kT
$$
where $T10 4 A trolley on a smooth surface is attached by springs to fixed blocks as shown in Fig. 4.1.  Fig. 4.1 The trolley oscillates horizontally about its equilibrium position with an amplitude of 12 cm. Fig. 4.2 shows the variation of the acceleration $a$ of the trolley with displacement $x$ from its equilibrium position. Friction between the trolley and the surface can be assumed to be negligible.  Fig. 4.2 (a) Describe the features of the line in Fig. 4.2 that demonstrate that the motion of the trolley is simple harmonic. ............................................................................................................................... .............................................................................................
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(b) Use Fig. 4.2 to determine the period $T$ of the oscillations of the trolley.
$$
T = \underline{\hspace{5cm}} \text{ s [3]}
$$
(c) (i) On the line of the graph of Fig. 4.2, label with the letter P one point where the kinetic energy of the trolley is zero. [1]
(ii) On the line of the graph of Fig. 4.2, label with the letter Q an approximate position of one point where the kinetic energy of the trolley is equal to the potential energy stored in the springs. 1
© UCLES 2021 9702/42/O/N/21 [Turn over12 5 (a) (i) When audio signals are transmitted over long distances, modulation of radio waves is used. Suggest a reason why modulation is used. ............................................................................................................................... ............................................................................................................................... [1] (ii) State a technical advantage and a technical disadvantage of using frequency modulation rather than amplitude modulation. advantage: ....................................................................................................................... ............................................................................................................................... di
13 6 (a) Define *electric potential*. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) An isolated conducting sphere in a vacuum has radius $r$ and is initially uncharged. It is then charged by friction so that it carries a final charge $Q$ . This charge can be considered to be acting at the centre of the sphere. By considering the electric potential at its surface, show that the capacitance $C$ of the sphere is given by $$ C = 4\pi\varepsilon_0
14 7 (a) An operational amplifier (op-amp) has two input terminals and one output terminal. State what is meant by the *gain* of an op-amp. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (b) State **two** effects of negative feedback on the gain of an amplifier circuit that uses an op-amp. 1. ............................................................................................................................... .............................
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(iii) Calculate the gain of the circuit in Fig. 7.1.
$$
\text{gain} = \underline{\hspace{6cm}} \quad [2]
$$
(iv) Determine the value of $V_{IN}$ when $V_{OUT}$ is +6.5 V.
$$
V_{IN} = \underline{\hspace{6cm}} \, \text{V} \quad [1]
$$
(v) Determine the value of $V_{OUT}$ when $V_{IN}$ is –5.4 V.
$$
V_{OUT} = \underline{\hspace{6cm}} \, \text{V} \quad [1]
$$
[Total: 10]
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8 Two long straight parallel wires P and Q carry currents into the plane of the paper, as shown in Fig. 8.1.
<div style="display: flex; justify-content: space-around; margin: 20px 0;">
<div>
<div>P</div>
<div>⊗</div>
<div>current $I$ </div>
</div>
<div>
<div>Q</div>
<div>⊗</div>
<div>current $2I$ </div>
</div>
</div>
Fig. 8.1
The current in P is $I$ and the current in Q is $2I$ .
(a) (i) On Fig. 8.1, draw an arrow to show the direction of the magnetic field at wire Q due to the current in wire P. Label this arrow B. [1]
(ii) On Fig. 8.1, draw another arrow to show the direction of the force acting on wire Q due to the current in wire P. Label this arrow F. [1]
(b) (i) State, with a reason, how the magnitude of the force acting on wire P compares wi17 9 (a) State what is meant by: (i) the photoelectric effect ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) work function energy. ............................................................................................................................... ............................................................................................................................... [1] (b) A polished calcium plate in a vacuum is investigat
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10 Fig. 10.1 shows a simple laminated iron-cored transformer consisting of a primary coil of 25000 turns and a secondary coil of 625 turns.
<div style="text-align: center;">
</div>
Fig. 10.1
The output potential difference (p.d.) $V_{OUT}$ is applied to a load resistor of resistance $640\,\Omega$ .
(a) (i) State the function of the iron core.
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(ii) Explain why the iron core is laminated.
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(ii) Calculate the root-mean-square (r.m.s.) current in the load resistor.
$$
\text{r.m.s. current} = \underline{\hspace{5cm}} \text{ A [1]}
$$
(iii) On Fig. 10.2, sketch the variation with time $t$ of the power $P$ dissipated in the load resistor for time $t = 0$ to $t = 40\,\text{ms}$ . Assume that $P = 0$ when $t = 0$ .
<div style="text-align: center;">
</div>
Fig. 10.2
[3]
(c) Explain, with reference to Fig.10.2, why the mean power in the load resistor is 70 W.
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21 11 (a) A piezoelectric transducer containing a quartz crystal is used to obtain diagnostic information about internal structures. Describe the function of the quartz crystal. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) (i) Define specific acoustic impedance. ......................................................
22 12 (a) Radioactive decay is both random and spontaneous. State what is meant by: (i) *random* ............................................................................................................................... ............................................................................................................................... [1] (ii) *spontaneous.* ............................................................................................................................... ............................................................................................................................... [1] (b) A sample of radioactive material contains atoms of an unstable nuclide X. The activity of the sample due to the atoms of X is A. The variation with ti
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(i) Use Fig. 12.1 to determine the half-life, in minutes, of nuclide X.
half-life = ………………………………………… min [3]
(ii) At time $t = 0$ , the mass of the atoms of X in the sample is $5.66 \times 10^{-7}$ kg.
Determine the nucleon number of X.
nucleon number = ………………………………………… 3
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