科目：物理 Physics (9702)
年份：2011 冬季
试卷：Paper 41
总页数：20
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 17: Oscillations, 18: Electric fields, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics
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Section A
Answer all the questions in the spaces provided.
For Examiner's Use
1 (a) A moon is in a circular orbit of radius $r$ about a planet. The angular speed of the moon in its orbit is $\omega$ . The planet and its moon may be considered to be point masses that are isolated in space.
Show that $r$ and $\omega$ are related by the expression
$$
r^3 \omega^2 = \text{constant}.
$$
Explain your working.
[3]
(b) Phobos and Deimos are moons that are in circular orbits about the planet Mars. Data for Phobos and Deimos are shown in Fig. 1.1.
<table>
<tr>
<th>moon</th>
<th>radius of orbit /m</th>
<th>period of rotation about Mars /hours</th>
</tr>
<tr>
<td>Phobos<br>Deimos</td>
<td> $9.39 \times 10^6$ <br> $1.99 \times 10^7$ </td>
<td>7.65</td>
</tr>
5 (i) Use data from Fig. 1.1 to determine 1. the mass of Mars, mass = ……………………………… kg [3] 2. the period of Deimos in its orbit about Mars. period = ……………………………… hours [3] (ii) The period of rotation of Mars about its axis is 24.6 hours. Deimos is in an equatorial orbit, orbiting in the same direction as the spin of Mars about its axis. Use your answer in (i) to comment on the orbit of Deimos. ……………………………………………………………………………………………………… [1] © UCLES 2011 9702/41/O/N/11 [Turn over For Examiner’s Use
6 2 (a) One assumption of the kinetic theory of gases is that gas molecules behave as if they are hard, elastic identical spheres. State two other assumptions of the kinetic theory of gases. 1. ............................................................................................................................... ............................................................................................................................ 2. ............................................................................................................................... ............................................................................................................................ [2] (b) Using the kinetic theory of gases, it can be shown that the product of the pressu
7 (c) (i) State what is meant by the *internal energy* of a substance. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [2] (ii) Use the equation in (b)(ii) to explain that, for an ideal gas, a change in internal energy $\Delta U$ is given by $$ \Delta U \propto \Delta T $$ where $\Delta T$ is the change in temperature of the gas. ............................................................................................................................
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3 A bar magnet is suspended from the free end of a helical spring, as illustrated in Fig. 3.1.
<div style="text-align: center;">
</div>
Fig. 3.1
One pole of the magnet is situated in a coil of wire. The coil is connected in series with a switch and a resistor. The switch is open.
The magnet is displaced vertically and then released. As the magnet passes through its rest position, a timer is started. The variation with time $t$ of the vertical displacement $y$ of the magnet from its rest position is shown in Fig. 3.2.
<div style="text-align: center;">
</div>
Fig. 3.2
At time $t = 4.0\,\text{s}$ , the switch is closed.
© UCLES 2011
9702/41/O/N/11
For Examiner's Use9
(a) Use Fig. 3.2 to
(i) state the evidence for the magnet to be undergoing free oscillations during the period $t = 0$ to $t = 4.0\,\text{s}$ ,
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(ii) state, with a reason, whether the damping after time $t = 4.0\,\text{s}$ is light, critical or heavy,
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............................................................................................................................... [2]
(iii) determine the10
4 Two small charged metal spheres A and B are situated in a vacuum. The distance between the centres of the spheres is 12.0 cm, as shown in Fig. 4.1.
<div style="text-align: center;">
</div>
Fig. 4.1 (not to scale)
The charge on each sphere may be assumed to be a point charge at the centre of the sphere.
Point P is a movable point that lies on the line joining the centres of the spheres and is distance $x$ from the centre of sphere A.
The variation with distance $x$ of the electric field strength $E$ at point P is shown in Fig. 4.2.
<div style="text-align: center;">
</div>
Fig. 4.2
© UCLES 2011 9702/41/O/N/11
For Examiner's Use11 (a) State the evidence provided by Fig. 4.2 for the statements that (i) the spheres are conductors, ............................................................................................................................... ............................................................................................................................... [1] (ii) the charges on the spheres are either both positive or both negative. ............................................................................................................................ ............................................................................................................................ [2] (b) (i) State the relation between electric field strength $E$ and potential gradient at a point. .
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5 Positively charged particles are travelling in a vacuum through three narrow slits $S_1$, $S_2$ and $S_3$, as shown in Fig. 5.1.
<div style="text-align: center;">
</div>
Fig. 5.1
Each particle has speed $v$ and charge $q$.
There is a uniform magnetic field of flux density $B$ and a uniform electric field of field strength $E$ in the region between the slits $S_2$ and $S_3$.
(a) State the expression for the force $F$ acting on a charged particle due to
(i) the magnetic field,
........................................................................................................................... [1]
(ii) the electric field.
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6 The variation with time $t$ of the output $V$ of an alternating voltage supply of frequency 50 Hz is shown in Fig. 6.1.
<div style="text-align: center;">
</div>
Fig. 6.1
(a) Use Fig. 6.1 to state
(i) the time $t_1$ ,
$$
t_1 = \underline{\hspace{5cm}} \text{ s [2]}
$$
(ii) the peak value $V_0$ of the voltage,
$$
V_0 = \underline{\hspace{5cm}} \text{ V [1]}
$$
(iii) the root-mean-square voltage $V_{\text{rms}}$ ,
$$
V_{\text{rms}} = \underline{\hspace{5cm}} \text{ V [1]}
$$
(iv) the mean voltage $\langle V \rangle$ .
$$
\langle V \rangle = \underline{\hspace{5cm}} \text{ V [1]}
$$
© UCLES 2011 9702/41/O/N/11 [Turn over]
For Examiner's Use14 (b) The alternating supply is connected in series with a resistor of resistance $2.4\,\Omega$ . Calculate the mean power dissipated in the resistor. power = ________________________ W [2] For Examiner's Use © UCLES 2011 9702/41/O/N/11
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7 (a) Explain how the line spectrum of hydrogen provides evidence for the existence of discrete electron energy levels in atoms.
...............................................................................................................................
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............................................................................................................................... [3]
(b) Some electron energy levels in atomic hydrogen are illustrated in Fig. 7.1.
-0.85 eV
────────────────
│ 16 (c) The light in a beam has a continuous spectrum of wavelengths from 400 nm to 700 nm. The light is incident on some cool hydrogen gas, as illustrated in Fig. 7.2. <div style="text-align: center;">  </div> Fig. 7.2 Using the values of wavelength in (b), state and explain the appearance of the spectrum of the emergent light. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ...................................................
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8 The isotope phosphorus-33 ( $^{33}_{15}\text{P}$ ) undergoes $\beta$ -decay to form sulfur-33 ( $^{33}_{16}\text{S}$ ), which is stable.
The half-life of phosphorus-33 is 24.8 days.
(a) (i) Define radioactive *half-life*.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(ii) Show that the decay constant of phosphorus-33 is $3.23 \times 10^{-7} \, \text{s}^{-1}$ .
[1]
(b) A pure sample of phosphorus-33 has an initial activity of $3.7 \times 1018
(c) After 30 days, the sample in (b) will contain phosphorus-33 and sulfur-33 nuclei.
Use your answers in (b) to calculate the ratio
$$
\frac{\text{number of phosphorus-33 nuclei after 30 days}}{\text{number of sulfur-33 nuclei after 30 days}}
$$
ratio = ................................................... [2]
For Examiner’s Use
© UCLES 2011 9702/41/O/N/1119 Section B Answer all the questions in the spaces provided. For Examiner's Use 9 (a) State two effects of negative feedback on the gain of an amplifier incorporating an operational amplifier (op-amp). 1. ............................................................................................................................... ............................................................................................................................ 2. ............................................................................................................................... ............................................................................................................................ [2] (b) An incomplete circuit diagram of a non-inverting amplifier using an
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(c) On Fig. 9.2, draw a graph to show the variation with input potential $V_{IN}$ of the output potential $V_{OUT}$. You should consider input potentials in the range 0 to +1.0 V.
<div style="text-align: center;">
</div>
Fig. 9.2
[2]
(d) The output of the amplifier circuit of Fig. 9.1 may be connected to a relay. State and explain one purpose of a relay.
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...............................................................................................................................
............................................................................................................................... [2]
© UCLES 2011
97021 10 (a) Cable television uses optic fibres for the transmission of signals. Suggest four advantages of optic fibres over coaxial cables for the transmission of data. 1. ............................................................................................................................ ............................................................................................................................ 2. ............................................................................................................................ ............................................................................................................................ 3. .................................................................................................................
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(c) An optic fibre has an attenuation per unit length of $0.2 \, \text{dB} \, \text{km}^{-1}$ .
A signal is transmitted along the optic fibre of length 30 km to a receiver. The noise power at the receiver is $9.3 \, \mu\text{W}$ .
The minimum acceptable signal-to-noise ratio at the receiver is 26 dB.
Calculate
(i) the minimum signal power at the receiver,
$$
\text{power} = \underline{\hspace{5cm}} \, \text{W [2]}
$$
(ii) the minimum input signal power to the optic fibre.
$$
\text{power} = \underline{\hspace{5cm}} \, \text{W [2]}
$$
For Examiner’s Use
© UCLES 2011 9702/41/O/N/1123
11 A simplified block diagram of a mobile phone handset is shown in Fig. 11.1.
For Examiner's Use
plaintext
aerial √
|
A
/ \
amplifier B
| |
modulator r.f.
amplifier
| |
parallel-to-serial demodulator
| |
C serial-to-
parallel
| |
a.f. DAC
amplifier |
| D
microphone loudspeaker
```
Fig. 11.1
(a) Name and state the function of
(i) block A,
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