Cambridge A Level Physics 9702 — 2008 Oct/Nov Paper 4 · Variant 1

1 A spherical planet has mass M and radius R. The planet may be assumed to be isolated in space and to have its mass concentrated at its centre. The planet spins on its axis with angular speed ω, as illustrated in Fig. 1.1. mass m R equator of planet pole of planet Fig. 1.1 A small object of mass m rests on the equator of the planet. The surface of the planet exerts a normal reaction force on the mass. (a) State formulae, in terms of M, m, R and ω, for (i) the gravitational force between the planet and the object, ..............................................................................................................................[1] (ii) the centripetal force required for circular motion of the small mass, ..............................................................................................................................[1] (iii) the normal reaction exerted by the planet on the mass. ..............................................................................................................................[1] (b) (i) Explain why the normal reaction on the mass will have different values at the equator and at the poles. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2] (ii) The radius of the planet is 6.4 × 106 m. It completes one revolution in 8.6 × 104 s. For Calculate the magnitude of the centripetal acceleration at Examiner’s Use 1. the equator, acceleration = .........................................m s–2 [2] 2. one of the poles. acceleration = .........................................m s–2 [1] (c) Suggest two factors that could, in the case of a real planet, cause variations in the acceleration of free fall at its surface. 1. ...................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... [2]

Mark scheme: 1 (a) (i) F = GMm / R2 B1 [1] (ii) F = mRω2 B1 [1] (iii) reaction force = GMm / R2 – mRω2 (allow e.c.f.) B1 [1] (b) (i) either value of R in expression Rω2 varies or mRω2 no longer parallel to GMm / R2 / normal to surface B1 becomes smaller as object approaches a pole / is zero at pole B1 [2] (ii) 1. acceleration = 6.4 × 106 × (2π / {8.6 × 104})2 C1 = 0.034 m s–2 A1 [2] 2. acceleration = 0 A1 [1] (c) e.g. ‘radius’ of planet varies density of planet not constant planet spinning nearby planets / stars (any sensible comments, 1 mark each, maximum 2) B2 [2]

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2 (a) Define specific latent heat of fusion. For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... ......................................................................................................................................[2] (b) Some crushed ice at 0 °C is placed in a funnel together with an electric heater, as shown in Fig. 2.1. joule- supply meter crushed ice heater funnel ××× beaker Fig. 2.1 The mass of water collected in the beaker in a measured interval of time is determined with the heater switched off. The mass is then found with the heater switched on. The energy supplied to the heater is also measured. For both measurements of the mass, water is not collected until melting occurs at a constant rate. The data shown in Fig. 2.2 are obtained. mass of water energy supplied time interval / g to heater / J / min heater switched off 16.6 0 10.0 heater switched on 64.7 18000 5.0 Fig. 2.2 (i) State why the mass of water is determined with the heater switched off. .................................................................................................................................. ..............................................................................................................................[1] (ii) Suggest how it can be determined that the ice is melting at a constant rate. For Examiner’s .................................................................................................................................. Use ..............................................................................................................................[1] (iii) Calculate a value for the specific latent heat of fusion of ice. latent heat = ..................................... kJ kg–1 [3]

Mark scheme: 2 (a) (Thermal) energy / heat required to convert unit mass of solid to liquid M1 at its normal melting point / without any change in temperature A1 [2] (reference to 1 kg or to ice → water scores max 1 mark) (b) (i) To make allowance for heat gains from the atmosphere B1 [1] (ii) e.g. constant rate of production of droplets from funnel constant mass of water collected per minute in beaker (any sensible suggestion, 1 mark) B1 [1] (iii) mass melted by heater in 5 minutes = 64.7 – ½ × 16.6 = 56.4 g C1 56.4 × 10–3 × L = 18 C1 L = 320 kJ kg–1 A1 [3] (Use of m = 64.7, giving L = 278 kJ kg–1, scores max 1 mark use of m = 48.1, giving L = 374 kJ kg–1, scores max 2 marks)

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3 The needle of a sewing machine is made to oscillate vertically through a total distance of For 22 mm, as shown in Fig. 3.1. Examiner’s Use 22 mm needle at its maximum height 8.0 mm cloth Fig. 3.1 The oscillations are simple harmonic with a frequency of 4.5 Hz. The cloth that is being sewn is positioned 8.0 mm below the point of the needle when the needle is at its maximum height. (a) State what is meant by simple harmonic motion. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (b) The displacement y of the point of the needle may be represented by the equation y = a cosωt. (i) Suggest the position of the point of the needle at time t = 0. ..............................................................................................................................[1] (ii) Determine the values of 1. a, a = .......................................... mm [1] 2. ω. ω = ..................................... rad s–1 [2] (c) Calculate, for the point of the needle, For Examiner’s (i) its maximum speed, Use speed = ........................................ m s–1 [2] (ii) its speed as it moves downwards through the cloth. speed = ........................................ m s–1 [3]

Mark scheme: 3 (a) acceleration / force (directly) proportional to displacement M1 and either directed towards fixed point or acceleration & displacement in opposite directions A1 [2] (b) (i) maximum / minimum height / 8 mm above cloth / 14 mm below cloth B1 [1] (ii) 1. a = 11 mm A1 [1] 2. ω = 2πf C1 = 2π × 4.5 = 28.3 rad s–1 (do not allow 1 s.f.) A1 [2] GCE A/AS LEVEL – October/November 2008 9702 04 (c) (i) v = ωa C1 = 28.3 × 11 × 10–3 = 0.31 m s–1 (do not allow 1 s.f.) A1 [2] (ii) v = ω √(a2 – y2) y = 3 mm C1 = 28.3 × 10–3 √(112 – 32) C1 = 0.30 m s–1 (allow 1 s.f.) A1 [3]

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4 (a) Write down an equation to represent the first law of thermodynamics in terms of the For heating q of a system, the work w done on the system and the increase ∆U in the Examiner’s internal energy. Use ......................................................................................................................................[1] (b) The pressure of an ideal gas is decreased at constant temperature. Explain what change, if any, occurs in the internal energy of the gas. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[3]

Mark scheme: 4 (a) ∆U = q + w (allow correct word equation) B1 [1] (b) either kinetic energy constant because temperature constant M1 potential energy constant because no intermolecular forces M1 so no change in internal energy A1 [3] or kinetic energy and potential energy both constant (M1) so no change in internal energy (A1) reason for either constant k.e. or constant p.e. given (A1)

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5 Two deuterium (21H) nuclei are travelling directly towards one another. When their separation For is large compared with their diameters, they each have speed v as illustrated in Fig. 5.1. Examiner’s Use v v deuterium deuterium nucleus nucleus Fig. 5.1 The diameter of a deuterium nucleus is 1.1 × 10–14 m. (a) Use energy considerations to show that the initial speed v of the deuterium nuclei must be approximately 2.5 × 106 m s–1 in order that they may come into contact. Explain your working. [3] (b) For a fusion reaction to occur, the deuterium nuclei must come into contact. Assuming that deuterium behaves as an ideal gas, deduce a value for the temperature of the deuterium such that the nuclei have an r.m.s. speed equal to the speed calculated in (a). temperature = .............................................. K [4] (c) Comment on your answer to (b). .......................................................................................................................................... ......................................................................................................................................[1]

Mark scheme: 5 (a) change/loss in kinetic energy = change/gain in electric potential energy B1 2 × ½mv2 = q2 / 4πε0r C1 2 × ½ × 2 × 1.67 × 10–27 × v2 = (1.6 × 10–19)2 / (4π × 8.85 × 10–12 × 1.1 × 10–14) M1 v = 2.5 × 106 m s–1 A0 [3] (b) pV = ½Nm<c2> and pV = NkT C1 ½ m<c2> = 3 2 kT (award 1 mark of first two if <c2> not used) C1 ½ × 2 × 1.67 × 10–27 × (2.5 × 106)2 = 3 2 × 1.38 × 10–23 × T C1 T = 5 × 108 K A1 [4] (c) e.g. this is very high temperature temperature found in stars (any sensible comment, 1 mark) (if T < 106 K, should comment that too low for fusion to occur) B1 [1]

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6 A simple iron-cored transformer is illustrated in Fig. 6.1. For Examiner’s Use laminated soft-iron core primary secondary coil coil Fig. 6.1 (a) Suggest why the core is (i) a continuous loop, .................................................................................................................................. ..............................................................................................................................[1] (ii) laminated. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2] (b) (i) State Faraday’s law of electromagnetic induction. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2] (ii) Use Faraday’s law to explain the operation of the transformer. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[3] (c) State two advantages of the use of alternating voltages for the transmission and use of For electrical energy. Examiner’s Use 1. ...................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... [2]

Mark scheme: 6 (a) (i) either prevent loss of magnetic flux or improves flux linkage with secondary B1 [1] (ii) reduces eddy current (losses) B1 reduces losses of energy (in core) B1 [2] (b) (i) (induced) e.m.f. proportional to / equal to M1 rate of change of (magnetic) flux (linkage) A1 [2] (ii) changing current in primary gives rise to (1) changing flux in core (1) flux links with the secondary coil (1) changing flux in secondary coil, inducing e.m.f. (1) GCE A/AS LEVEL – October/November 2008 9702 04 (any three, 1 each to max 3) B3 [3] (c) e.g. can change voltage easily / efficiently high voltage transmission reduces power losses (any two sensible suggestions, 1 each) B2 [2]

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7 (a) State three pieces of evidence provided by the photoelectric effect for a particulate For nature of electromagnetic radiation. Examiner’s Use 1. ...................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... 3. ...................................................................................................................................... .......................................................................................................................................... [3] (b) (i) Briefly describe the concept of a photon. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2] (ii) Explain how lines in the emission spectrum of gases at low pressure provide evidence for discrete electron energy levels in atoms. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[2] (c) Three electron energy levels in atomic hydrogen are represented in Fig. 7.1. For Examiner’s Use increasing energy Fig. 7.1 The wavelengths of the spectral lines produced by electron transitions between these three energy levels are 486 nm, 656 nm and 1880 nm. (i) On Fig. 7.1, draw arrows to show the electron transitions between the energy levels that would give rise to these wavelengths. Label each arrow with the wavelength of the emitted photon. [3] (ii) Calculate the maximum change in energy of an electron when making transitions between these levels. energy = ...............................................J [3]

Mark scheme: 7 (a) e.g. ‘instantaneous’ emission (of electrons) threshold frequency below which no emission (max) electron energy dependent on frequency (max) electron energy not dependent on intensity rate of emission (of electrons) depends on intensity (any three sensible suggestions, 1 each) B3 [3] (b) (i) ‘packet’ / quantum of energy M1 of electromagnetic energy / radiation A1 [2] (ii) discrete wavelengths mean photons have particular energies M1 energy of photon determined by energy change of (orbital) electron M1 so discrete energy levels A0 [2] (c) (i) three energy changes shown correctly B1 arrows ‘pointing’ in correct direction B1 wavelengths correctly identified B1 [3] (ii) chooses λ = 486 nm C1 ∆E = hc / λ C1 = (6.63 × 10–34 × 3.0 × 108) / (4.86 × 10–9) = 4.09 × 10–19 J (allow 2 s.f.) A1 [3]

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8 (a) Describe what is meant by a magnetic field. For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[3] (b) A small mass is placed in a field of force that is either electric or magnetic or gravitational. State the nature of the field of force when the mass is (i) charged and the force is opposite to the direction of the field, ..............................................................................................................................[1] (ii) uncharged and the force is in the direction of the field, ..............................................................................................................................[1] (iii) charged and there is a force only when the mass is moving, ..............................................................................................................................[1] (iv) charged and there is no force on the mass when it is stationary or moving in a particular direction. ..............................................................................................................................[1]

Mark scheme: 8 (a) region (of space) / area where B1 a force is experienced by M1 current-carrying conductor / moving charge / permanent magnet A1 [3] (b) (i) electric B1 [1] (ii) gravitational B1 [1] (iii) magnetic B1 [1] (iv) magnetic B1 [1] GCE A/AS LEVEL – October/November 2008 9702 04 Section B

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9 Different frequencies and wavelengths are used in different channels of communication. Suggest why (a) infra-red radiation rather than visible light is usually used with optic fibres, .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (b) the base stations in mobile phone networks operate on UHF, .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2] (c) for satellite communication, frequencies of the order of GHz are used, with the uplink having a different frequency to the downlink. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[2]

Mark scheme: 9 (a) IR has less attenuation (per unit length) B1 fewer (repeater) amplifiers / longer uninterrupted length B1 [2] (b) either limited range B1 (so) cells do not overlap (appreciably) B1 [2] or short wavelength (B1) so convenient length aerial (on mobile phone) (B1) (c) large bandwidth / large information carrying capacity B1 different so that uplink signal not swamped by downlink B1 [2]

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10 (a) The circuit for an amplifier incorporating an ideal operational amplifier (op-amp) is shown For in Fig. 10.1. Examiner’s Use R2 R1 +9 V – P + VIN –9 V VOUT Fig. 10.1 (i) State 1. the name of this type of amplifier circuit, ..............................................................................................................................[1] 2. why the point P is referred to as a virtual earth. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[3] (ii) Show that the gain G of this amplifier circuit is given by the expression R2 G = – ––– . R1 Explain your working. [4] (b) The circuit of Fig. 10.1 is modified by connecting a light-dependent resistor (LDR) as For shown in Fig. 10.2. Examiner’s Use R2 R1 +9 V – + VIN = +1.2 V –9 V VOUT V Fig. 10.2 The resistances R1 and R2 are 5.0 kΩ and 50 kΩ respectively. The input voltage VIN is +1.2 V. A high-resistance voltmeter measures the output VOUT. The circuit is used to monitor low light intensities. (i) Determine the voltmeter reading for light intensities such that the LDR has a resistance of 1. 100 kΩ, reading = .............................................. V [3] 2. 10 kΩ. reading = .............................................. V [2] (ii) The light incident on the LDR is provided by a single lamp. Use your answers in (i) For to describe and explain qualitatively the variation of the voltmeter reading as the Examiner’s lamp is moved away from the LDR. Use .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[3]

Mark scheme: 10 (a) (i) 1. inverting (amplifier) B1 [1] 2. gain of op-amp is very large / infinite B1 non-inverting input is at earth / 0 V B1 for amplifier not to saturate, P must be at about earth / 0 V B1 [3] (ii) input resistance is very large B1 (so) current in R1 = current in R2 B1 I = VIN / R1 B1 I = – VOUT / R2 (minus sign can be in either of the equations) B1 hence gain = VOUT / VIN = –R2 / R1 A0 [4] (b) (i) 1. feedback resistance = 33.3 kΩ C1 gain (= 33.3 / 5) = 6.66 C1 VOUT (= 6.66 × 1.2) = 8.0 V (+ or – acceptable, allow 1 s.f.) A1 [3] 2. feedback resistance = 8.33 kΩ C1 VOUT (= {6.66 × 1.2} / 5) = 2.0 V (+ or – acceptable, allow 1 s.f.) A1 [2] (ii) (Increase in lamp-LDR distance gives) decrease in intensity M1 Feedback / LDR resistance increases M1 voltmeter reading increases / becomes more negative A1 [3]

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11 (a) Distinguish between the images produced by CT scanning and X-ray imaging. For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[3] (b) By reference to the principles of CT scanning, suggest why CT scanning could not be developed before powerful computers were available. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[5]

Mark scheme: 11 (a) CT image: (thin) slice (through structure) B1 any further detail e.g. built up from many ‘slices’ / 3-D image B1 X-ray image: ‘shadow’ image (of whole structure) / 2-D image B1 [3] (b) X-ray image of slice taken from many different angles (1) these images are combined (and processed) (1) repeated for many different slices (1) to build up a 3-D image (1) 3-D image can be rotated (1) computer required to store and process huge quantity of data (1) (any five, 1 each to max 5) B5 [5]

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