AS & A Level Physics - 9702 Paper 4 2014 Winter Zone 2

An isolated spherical planet has a diameter of $6.8 \times 10^6$ m. Its mass of $6.4 \times 10^{23}$ kg may be assumed to be a point mass at the centre of the planet.

(a) Show that the gravitational field strength at the surface of the planet is $3.7 \, \text{N} \, \text{kg}^{-1}$. [2]

(b) A stone of mass $2.4$ kg is raised from the surface of the planet through a vertical height of $1800$ m.

Use the value of field strength given in (a) to determine the change in gravitational potential energy of the stone.

Explain your working.   [3]

(c) A rock, initially at rest at infinity, moves towards the planet. At point P, its height above the surface of the planet is $3.5 D$, where $D$ is the diameter of the planet, as shown in Fig. 1.1.

Calculate the speed of the rock at point P, assuming that the change in gravitational potential energy is all transferred to kinetic energy.   [4]

(a) State what is meant by an ideal gas.   [1]

(b) A storage cylinder for an ideal gas has a volume of $3.0 \times 10^{-4} \text{ m}^3$. The gas is at a temperature of $23^{\circ}$C and a pressure of $5.0 \times 10^7$ Pa.

(i) Show that the amount of gas in the cylinder is 6.1 mol. [2]

(ii) The gas leaks slowly from the cylinder so that, after a time of 35 days, the pressure has reduced by 0.40%. The temperature remains constant. Calculate the average rate, in atoms per second, at which gas atoms escape from the cylinder.   [4]

(a) State what is meant by simple harmonic motion.

(b) A small ball rests at point P on a curved track of radius \( r \), as shown in Fig. 4.1.

The ball is moved a small distance to one side and is then released. The horizontal displacement \( x \) of the ball is related to its acceleration \( a \) towards P by the expression

\[ a = -\frac{gx}{r} \]

where \( g \) is the acceleration of free fall.

(i) Show that the ball undergoes simple harmonic motion.

(ii) The radius \( r \) of curvature of the track is 28 cm.

Determine the time interval \( \tau \) between the ball passing point P and then returning to point P.

(c) The variation with time \( t \) of the displacement \( x \) of the ball in (b) is shown in Fig. 4.2.

Some moisture now forms on the track, causing the ball to come to rest after approximately 15 oscillations.

On the axes of Fig. 4.2, sketch the variation with time \( t \) of the displacement \( x \) of the ball for the first two periods after the moisture has formed. Assume the moisture forms at time \( t = 0 \). [3] 

(a) Define \textit{electric potential} at a point.
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(b) An isolated solid metal sphere is positively charged.
The variation of the potential $V$ with distance $x$ from the centre of the sphere is shown in Fig. 5.1.



Use Fig. 5.1 to suggest
(i) why the radius of the sphere cannot be greater than 1.0 cm,
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(ii) that the charge on the sphere behaves as if it were a point charge.
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(c) Assuming that the charge on the sphere does behave as a point charge, use data from Fig. 5.1 to determine the charge on the sphere.
charge = .............................................................. C [2]

A stiff straight copper wire XY is held fixed in a uniform magnetic field of flux density $2.6 imes 10^{-3}$ T, as shown in Fig. 6.1.
The wire XY has length 4.7 cm and makes an angle of 34° with the magnetic field.
(a) Calculate the force on the wire due to a constant current of 5.4 A in the wire.
force = .................. N [2]
(b) The current in the wire is now changed to an alternating current of r.m.s. value 1.7 A.
Determine the total variation in the force on the wire due to the alternating current.
variation in force = .................. N [3]

(a) The mean value of an alternating current is zero. Explain
(i) why an alternating current gives rise to a heating effect in a resistor,
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(ii) by reference to heating effect, what is meant by the root-mean-square (r.m.s.) value of an alternating current.
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(b) A simple iron-cored transformer is illustrated in Fig. 7.1.

(i) State Faraday’s law of electromagnetic induction.
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(ii) Use Faraday’s law to explain why the current in the primary coil is not in phase with the e.m.f. induced in the secondary coil.
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White light is incident on a cloud of cool hydrogen gas, as illustrated in Fig. 8.1.



The spectrum of the light emerging from the gas cloud is found to contain a number of dark lines.

(a) Explain why these dark lines occur.
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(b) Some electron energy levels in a hydrogen atom are illustrated in Fig. 8.2.



One dark line is observed at a wavelength of 435 nm.

(i) Calculate the energy, in eV, of a photon of light of wavelength 435 nm.
energy = .............................................................. eV [4]

(ii) On Fig. 8.2, draw an arrow to indicate the energy change that gives rise to this dark line. [1]

One likely means by which nuclear fusion may be achieved on a practical scale is the D-T reaction.
(a) State what is meant by nuclear fusion.
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(b) In the D-T reaction, a deuterium ($^2_1$H) nucleus fuses with a tritium ($^3_1$H) nucleus to form a helium-4 ($^4_2$He) nucleus. The nuclear equation for the reaction is
$$^2_1 \text{H} + ^3_1 \text{H} \rightarrow ^4_2 \text{He} + ^1_0 \text{n} + \text{energy}$$
Some data for this reaction are given in Fig. 9.1.

[Table_1]

Fig. 9.1
(i) Calculate the energy, in MeV, equivalent to 1.00 u. Explain your working.

energy = .................................................. MeV [3]

(ii) Use data from Fig. 9.1 and your answer in (i) to determine the energy released in this D-T reaction.

energy = .................................................. MeV [2]

(iii) Suggest why, for the D-T reaction to take place, the temperature of the deuterium and the tritium must be high.
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(a) An ideal operational amplifier (op-amp) has infinite open-loop gain and infinite input resistance (impedance).
State three further properties of an ideal op-amp.
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(b) The circuit of Fig. 10.1 is used to detect changes in temperature.

The voltmeter has infinite resistance. The variation with temperature \(\theta\) of the resistance \(R\) of the thermistor is shown in Fig. 10.2.

(i) When the thermistor is at a temperature of 1.0\(^{\circ}\)C, the voltmeter reads +1.0V. Show that, for the thermistor at 1.0\(^{\circ}\)C, the potential at A is -0.20V.
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(ii) The potential at A remains at -0.20V. Determine the voltmeter reading for a thermistor temperature of 15\(^{\circ}\)C.
voltmeter reading = ............................................................... V [2]
(c) The voltmeter reading for a thermistor temperature of 29\(^{\circ}\)C is 0.35V.
(i) Assuming a linear change of voltmeter reading with change of temperature over the range 1\(^{\circ}\)C to 29\(^{\circ}\)C, calculate the voltmeter reading at 15\(^{\circ}\)C.
voltmeter reading = ............................................................... V [1]
(ii) Suggest why your answers in (b)(ii) and (c)(i) are not the same.
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The use of X-rays in medical diagnosis gives rise to an increased exposure of the patient to radiation. Explain why
(a) an aluminium filter may be placed in the X-ray beam when producing an X-ray image of a patient, ................................................................................................................................................
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(b) the radiation dose received by a patient is different for a CT scan from that for a simple X-ray image. ................................................................................................................................................
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(a) Information may be carried by different channels of communication.

State one application, in each case, where information is carried using

(i) microwaves,
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(ii) coaxial cables,
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(iii) wire pairs.
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(b) A station on Earth transmits a signal of initial power 3.1 kW to a geostationary satellite. The attenuation of the signal received by the satellite is 190 dB.

(i) Calculate the power of the signal received by the satellite.
power = ........................................ kW [2]

(ii) By reference to your answer in (i), state and explain the changes made to the signal before transmission back to Earth.
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A simplified block diagram of a mobile phone handset is shown in Fig. 13.1.
[Image_1: Fig. 13.1]
State the purpose of
(a) the switch, ..........................................................................................................................................................
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(b) the tuning circuit.
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