科目：物理 Physics (9702)
年份：2014 夏季
试卷：Paper 42
总页数：20
章节：12-13: Circular Motion & Gravitational Fields, 14-16: Temperature, Ideal Gases & Thermodynamics, 18: Electric fields, 20: Magnetic fields, 21: Alternating currents, 22: Quantum physics, 23: Nuclear physics, 24: Medical physics, 25: Astronomy and cosmology
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Section A
Answer all the questions in the spaces provided.
1 The mass $M$ of a spherical planet may be assumed to be a point mass at the centre of the planet.
(a) A stone, travelling at speed $v$ , is in a circular orbit of radius $r$ about the planet, as illustrated in Fig.1.1.
<div style="text-align: center;">
<br/>
Fig.1.1
</div>
Show that the speed $v$ is given by the expression
$$
v = \sqrt{\left(\frac{GM}{r}\right)}
$$
where $G$ is the gravitational constant.
Explain your working.
[2]
© UCLES 2014 9702/42/M/J/14
Note: The image placeholder (`image_placeholder.png`) is used to represent the diagram shown in the original document. In a real implementation, this would be replaced with the actual image file or embedded SVG/HTML representation.5 (b) A second stone, initially at rest at infinity, travels towards the planet, as illustrated in Fig.1.2. Fig.1.2 (not to scale) The stone does not hit the surface of the planet. (i) Determine, in terms of the gravitational constant $G$ and the mass $M$ of the planet, the speed $V_0$ of the stone at a distance $x$ from the centre of the planet. Explain your working. You may assume that the gravitational attraction on the stone is due only to the planet. [3] (ii) Use your answer in (i) and the expression in (a) to explain whether this stone could enter a circular orbit about the planet. ............................................................................................................................... .....................................................................
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2 A constant mass of an ideal gas has a volume of $3.49 \times 10^3 \, \text{cm}^3$ at a temperature of $21.0^\circ \text{C}$ . When the gas is heated, 565 J of thermal energy causes it to expand to a volume of $3.87 \times 10^3 \, \text{cm}^3$ at $53.0^\circ \text{C}$ . This is illustrated in Fig. 2.1.
<div style="text-align: center;">
<table>
<tr>
<td> $3.49 \times 10^3 \, \text{cm}^3$ <br> $21.0^\circ \text{C}$ </td>
<td> $\xrightarrow{565 \, \text{J}}$ </td>
<td> $3.87 \times 10^3 \, \text{cm}^3$ <br> $53.0^\circ \text{C}$ </td>
</tr>
</table>
<p>Fig. 2.1</p>
</div>
(a) Show that the initial and final pressures of the gas are equal.
[2]
(b) The pressure of the gas is $4.20 \times 10^5 \, \text{Pa}$ .
For this heating of the gas,
(i) calculate th7 (ii) use the first law of thermodynamics and your answer in (i) to determine the change in internal energy of the gas. change in internal energy = ………………………………………… J [2] (c) Explain why the change in kinetic energy of the molecules of this ideal gas is equal to the change in internal energy. ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ………………………………………………………………………………………………………… ……………………………………………………………………………………………………… [3] © UCLES 2014 9702/42/M/J/14 [Turn over
8 3 A microwave cooker uses electromagnetic waves of frequency 2450 MHz. The microwaves warm the food in the cooker by causing water molecules in the food to oscillate with a large amplitude at the frequency of the microwaves. (a) State the name given to this phenomenon. ........................................................................................................................... [1] (b) The effective microwave power of the cooker is 750 W. The temperature of a mass of 280 g of water rises from 25 °C to 98 °C in a time of 2.0 minutes. Calculate a value for the specific heat capacity of the water. specific heat capacity = ........................................ J kg⁻¹ K⁻¹ [3] (c) The value of the specific heat capacity determined from the data in (b) is greater th
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4 A helium nucleus contains two protons.
In a model of the helium nucleus, each proton is considered to be a charged point mass. The separation of these point masses is assumed to be $2.0 \times 10^{-15} \, \text{m}$ .
(a) For the two protons in this model, calculate
(i) the electrostatic force,
electrostatic force = ………………………………………… N [2]
(ii) the gravitational force.
gravitational force = ………………………………………… N [2]
(b) Using your answers in (a), suggest why
(i) there must be some other force between the protons in the nucleus,
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
…………………………………………………………………………………………………………
……………………………………………………………………………………………………… [3]
(ii) this additional force must have a short range.
………………………………………………………………………………………10 5 A Hall probe is placed a distance $d$ from a long straight current-carrying wire, as illustrated in Fig. 5.1.  Fig. 5.1 The direct current in the wire is 4.0 A. Line XY is normal to the wire. The Hall probe is rotated about the line XY to the position where the reading $V_H$ of the Hall probe is maximum. (a) The Hall probe is now moved away from the wire, along the line XY. On the axes of Fig. 5.2, sketch a graph to show the variation of the Hall voltage $V_H$ with distance $x$ of the probe from the wire. Numerical values are not required on your sketch.  Fig. 5.2 [2] © UCLES 2014 9702/42/M/J/14
11 (b) The Hall probe is now returned to its original position, a distance $d$ from the wire. At this point, the magnetic flux density due to the current in the wire is proportional to the current. For a direct current of 4.0 A in the wire, the reading of the Hall probe is 3.5 mV. The direct current is now replaced by an alternating current of root-mean-square (r.m.s.) value 4.0 A. The period of this alternating current is $T$. On the axes of Fig. 5.3, sketch the variation with time $t$ of the reading of the Hall voltage $V_H$ for two cycles of the alternating current. Give numerical values for $V_H$, where appropriate. <div style="text-align: center;">  <br/> Fig. 5.3 <br/> [3] </div> (c) A student suggests that the Hall probe in (a) is replaced with a
12 6 (a) Explain the use of a uniform electric field and a uniform magnetic field for the selection of the velocity of a charged particle. You may draw a diagram if you wish. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (b) Ions, all of the same isotope, are travelling in a vacuum with a speed of $9.6 \times 10^4 \, \text
13 (i) Determine the mass, in u, of the ions in path B. mass = ................................................... u [4] (ii) Suggest and explain quantitatively a reason for the difference in radii of the paths A and B of the ions. ............................................................................................................... ............................................................................................................... ............................................................................................................... ............................................................................................................... [3] © UCLES 2014 9702/42/M/J/14 [Turn over
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7 (a) Define the radian.
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [2]
(b) A telescope gives a clear view of a distant object when the angular displacement between the edges of the object is at least $9.7 \times 10^{-6}$ rad.
(i) The Moon is approximately $3.8 \times 10^5$ km from Earth.
Estimate the minimum diameter of a circular crater on the Moon’s surface that can be seen using the telescope.
diameter = ...................................15 8 Light of wavelength 590 nm is incident normally on a surface, as illustrated in Fig. 8.1. Fig. 8.1 The power of the light is 3.2 mW. The light is completely absorbed by the surface. (a) Calculate the number of photons incident on the surface in 1.0 s. number = ………………………………………… [3] (b) Use your answer in (a) to determine (i) the total momentum of the photons arriving at the surface in 1.0 s, momentum = ………………………………………… kg m s⁻¹ [3] (ii) the force exerted on the surface by the light. force = ………………………………………… N 1 © UCLES 2014 9702/42/M/J/14 [Turn over
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9 Some water becomes contaminated with radioactive iodine-131 ( $^{131}_{53}\text{I}$ ).
The activity of the iodine-131 in 1.0 kg of this water is 460 Bq.
The half-life of iodine-131 is 8.1 days.
(a) Define radioactive *half-life*.
............................................................................................................................
............................................................................................................................
............................................................................................................................ [2]
(b) (i) Calculate the number of iodine-131 atoms in 1.0 kg of this water.
number = ..........................................................................................17
(c) An acceptable limit for the activity of iodine-131 in water has been set as $170 \, \text{Bq} \, \text{kg}^{-1}$ .
Calculate the time, in days, for the activity of the contaminated water to be reduced to this acceptable level.
time = ………………………………………… days [3]
© UCLES 2014 9702/42/M/J/14 [Turn over18
Section B
Answer all the questions in the spaces provided.
10 (a) State the function of a comparator circuit incorporating an operational amplifier (op-amp).
...............................................................................................................................
...............................................................................................................................
...............................................................................................................................
............................................................................................................................... [3]
(b) An ideal op-amp is incorporated into the circuit of Fig. 10.1.
+1.5 V
|
| 1.2 kΩ
| ┌───┐
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(iii) The variation with time $t$ of the potential $V_{IN}$ at the inverting input of the op-amp is shown in Fig. 10.2.
Fig. 10.2
1. On the axes of Fig. 10.2, draw the variation with time $t$ of the output potential of the op-amp. [3]
2. State whether each diode is emitting light or is not emitting light at time $t_1$ and at time $t_2$.
At time $t_1$, diode R will …………………………… and diode G will …………………………….
At time $t_2$, diode R will …………………………… and diode G will ……………………………. [2]
© UCLES 2014 9702/42/M/J/14 [Turn over20 11 (a) Distinguish between an X-ray image of a body structure and a CT scan. X-ray image: ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... CT scan: ...........................................................................................
21 (i) Calculate the thickness of copper required to reduce the intensity of the emergent beam to $0.25I_0$ . thickness = ……………………………………… mm [2] (ii) An aluminium filter of thickness 2.4 mm is now placed in the X-ray beam, together with the copper filter in (i). Calculate the fraction of the incident intensity that emerges after passing through the two filters. fraction = ……………………………………… [2] (iii) Express your answer in (ii) as a gain in decibels (dB). gain = ……………………………………… dB [3] © UCLES 2014 9702/42/M/J/14 [Turn over
22 12 Two people, living in different regions of the Earth, communicate either using a link provided by a geostationary satellite or using optic fibres. (a) (i) Explain what is meant by a geostationary satellite. ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... ............................................................................................................................... [3] (ii) The uplink frequency for communication with the satellite i
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