Cambridge A Level Physics 9702 — 2018 May/June Paper 4 · Variant 3

1 (a) State Newton’s law of gravitation. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) A distant star is orbited by several planets. Each planet has a circular orbit with a different radius. (i) Each planet orbits at constant speed. Explain whether the planets are in equilibrium. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[1] (ii) The radius of the orbit of a planet is R and the orbital period is T. Data for some of the planets are given in Fig. 1.1. planet R / m T 2 / s2 c 9.6 × 1010 2.5 × 1011 e 4.0 × 1011 1.8 × 1013 g 2.1 × 1012 2.6 × 1015 Fig. 1.1 The relationship between R and T is given by the expression R 3 = kT 2. 1. Show that the constant k is given by the expression GM k = 4π2 where G is the gravitational constant and M is the mass of the star. [3] 2. Use data from Fig. 1.1 for the three planets and the expression for k to calculate the mass M of the star. M = ......................................................kg [3] [Total: 9]

Mark scheme: 1(a) force proportional to product of masses and inversely proportional to square of separation B1 idea of force between point masses B1 1(b)(i) velocity changes/direction of motion changes/there is an acceleration/there is a resultant force so not in equilibrium B1 1(b)(ii)1. gravitational force equals/is centripetal force C1 GMm / R2 = mRω2 and ω = 2π / T or Gm / R2 = mv2 / R and v = 2πr / T or GMm / R2 = mR (2π / T)2 M1 convincing algebra leading to k = GM / 4π2 A1 1(b)(ii)2. correct use of R3 / T2 for one planet (c gives 3.54 × 1021; e and g both give 3.56 × 1021) C1 3.5(5) × 1021 = (6.67 × 10–11 × M) / 4π2 M = 2.1 × 1033 kg A1 two or three values of R3 / T2 correctly calculated and used in a valid way to find a value for M based on more than one k B1

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2 A metal plate is made to vibrate vertically by means of an oscillator, as shown in Fig. 2.1. sand plate direction of oscillations oscillator Fig. 2.1 Some sand is sprinkled on to the plate. The variation with displacement y of the acceleration a of the sand on the plate is shown in Fig. 2.2. 5 4 a / m s–2 3 2 1 0 –10 –8 –6 –4 –2 0 2 4 6 8 10 y / mm –1 –2 –3 –4 –5 Fig. 2.2 (a) (i) Use Fig. 2.2 to show how it can be deduced that the sand is undergoing simple harmonic motion. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] (ii) Calculate the frequency of oscillation of the sand. frequency = ..................................................... Hz [2] (b) The amplitude of oscillation of the plate is gradually increased beyond 8 mm. The frequency is constant. At one amplitude, the sand is seen to lose contact with the plate. For the plate when the sand first loses contact with the plate, (i) state the position of the plate, .......................................................................................................................................[1] (ii) calculate the amplitude of oscillation. amplitude = ................................................... mm [3] [Total: 8]

Mark scheme: 2(a)(i) B1 negative gradient shows acceleration and displacement are in opposite directions B1 2(a)(ii) a = –ω2y and ω = 2πf 4.5 = (2π × f)2 × 8.0 × 10–3 (or other valid read-off) C1 f = 3.8 Hz A1 2(b)(i) maximum displacement upwards/above rest/above the equilibrium position B1 2(b)(ii) (just leaves plate when) acceleration = 9.81 m s–2 C1 9.81 = (2π × 3.8)2 × y0 or 9.81 = 563 × y0 C1 amplitude = 17 mm A1

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3 (a) (i) State what is meant by the internal energy of a system. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] (ii) Explain why, for an ideal gas, the change in internal energy is directly proportional to the change in thermodynamic temperature of the gas. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[3] (b) A cylinder of volume 1.8 × 104 cm3 contains helium gas at pressure 6.4 × 106 Pa and temperature 25 °C. Helium gas may be considered to be an ideal gas consisting of single atoms. Calculate the number of helium atoms in the cylinder. number = ...........................................................[3] [Total: 8]

Mark scheme: 3(a)(i) sum of potential and kinetic energies (of molecules/atoms/particles) B1 (energy of) molecules/atoms/particles in random motion B1 3(a)(ii) (in ideal gas) no intermolecular forces so no potential energy B1 internal energy is (solely) kinetic energy (of particles) B1 (mean) kinetic energy (of particles) proportional to (thermodynamic) temperature of gas B1 3(b) pV = NkT C1 6.4 × 106 × 1.8 × 104 × 10–6 = N × 1.38 × 10–23 × 298 C1 or pV = nRT and N = n × NA (C1) 6.4 × 106 × 1.8 × 104 × 10–6 = n × 8.31 × 298 n = 46.5 (mol) N = 46.5 × 6.02 × 1023 (C1) N = 2.8 × 1025 A1

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4 Piezo-electric transducers are used for the generation of ultrasonic waves. (a) State one other use, apart from in ultrasound, of piezo-electric transducers. ................................................................................................................................................... ...............................................................................................................................................[1] (b) Explain the main principles behind the use of ultrasound to obtain diagnostic information about internal body structures. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[6] [Total: 7]

Mark scheme: 4(a) e.g. microphone weighing scales/pressure sensor lighters/spark generation watches/clocks/regulation of time B1 4(b) pulses (of ultrasound) B1 reflected at boundaries (between media) B1 (reflected pulses) detected by (ultrasound) generator B1 Any three from: • time delay (between transmission and receipt) gives information about depth (of boundary) • intensity of reflected pulse gives information about (nature of) boundary • gel used to minimise reflection at skin/maximise transmission into skin • degree of reflection depends upon impedances of two media (at boundary) B3

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5 A geostationary satellite orbits the Earth with a period of 24 hours. (a) State (i) the direction of the orbit about the Earth, .......................................................................................................................................[1] (ii) the position of the satellite relative to the Earth’s surface, .......................................................................................................................................[1] (iii) a typical frequency for communication between the satellite and Earth. frequency = ..................................................... Hz [1] (b) A signal transmitted from Earth to a satellite has an initial power of 3.0 kW. The signal power received by the satellite is attenuated by 195 dB. (i) Calculate the signal power received by the satellite. power = ...................................................... W [3] (ii) By reference to your answer in (i), explain why different frequencies are used for the up-link and the down-link in communication with the satellite. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] [Total: 8]

Mark scheme: 5(a)(i) west to east B1 5(a)(ii) above the Equator B1 5(a)(iii) value in range (1–300) × 109 Hz A1 5(b)(i) gain / dB = 10 lg (P2 / P1) C1 –195 = 10 lg (P / 3000) or 195 = 10 lg (3000 / P) C1 power = 9.5 × 10–17 W A1 5(b)(ii) up-link has been (greatly) attenuated (before reaching satellite) or down-link signal must be (greatly) amplified (before transmission back to Earth) or up-link has (much) smaller intensity/power than down-link B1 (different frequency) prevents down-link (signal) swamping up-link (signal) B1

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6 (a) State what is meant by electric field strength. ................................................................................................................................................... ...............................................................................................................................................[1] (b) An isolated metal sphere A of radius 26 cm is positively charged. Sphere A is shown in Fig. 6.1. charged sphere A 26 cm Fig. 6.1 Electrical breakdown (a spark) occurs when the electric field strength at the surface of the sphere exceeds 2.0 × 104 V m–1. Calculate the maximum charge Q that can be stored on the sphere. Q = ....................................................... C [2] (c) A second isolated metal sphere B, also with charge +Q, has a radius of 52 cm. Calculate the additional charge, in terms of Q, that may be stored on this sphere before electrical breakdown occurs. additional charge = ...........................................................[2] [Total: 5]

Mark scheme: 6(a) force per unit charge B1 6(b) E = Q / (4πε0r2) C1 2.0 × 104 = Q / (4π × 8.85 × 10–12 × 0.262) charge = 1.5 × 10–7 C A1 6(c) charge (= Q [52 / 26]2) = 4Q C1 additional charge = 3Q A1

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7 (a) Explain what is meant by the capacitance of a parallel plate capacitor. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[3] (b) A parallel plate capacitor C is connected into the circuit shown in Fig. 7.1. X Y S A 120 V C Fig. 7.1 When switch S is at position X, the battery of electromotive force 120 V and negligible internal resistance is connected to capacitor C. When switch S is at position Y, the capacitor C is discharged through the sensitive ammeter. The switch vibrates so that it is first in position X, then moves to position Y and then back to position X fifty times each second. The current recorded on the ammeter is 4.5 μA. Determine (i) the charge, in coulomb, passing through the ammeter in 1.0 s, charge = ....................................................... C [1] (ii) the charge on one plate of the capacitor, each time that it is charged, charge = ....................................................... C [1] (iii) the capacitance of capacitor C. capacitance = ....................................................... F [2] (c) A second capacitor, having a capacitance equal to that of capacitor C, is now placed in series with C. Suggest and explain the effect on the current recorded on the ammeter. ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] [Total: 9]

Mark scheme: 7(a) (capacitance =) charge / potential M1 charge is (numerically equal to) charge on one plate A1 potential is potential difference between plates A1 7(b)(i) 4.5 × 10–6 C A1 7(b)(ii) 9.0 × 10–8 C A1 7(b)(iii) capacitance = (9.0 × 10–8) / 120 C1 = 7.5 × 10–10 F A1 7(c) total capacitance is halved B1 current is halved B1

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8 (a) Negative feedback is often used in amplifiers incorporating an operational amplifier (op-amp). State (i) what is meant by negative feedback, ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] (ii) two effects of negative feedback on the gain of an amplifier. 1. ....................................................................................................................................... ........................................................................................................................................... 2. ....................................................................................................................................... ........................................................................................................................................... [2] (b) An ideal op-amp is incorporated into the amplifier circuit shown in Fig. 8.1. 9600 Ω +6 V 800 Ω – + VIN –6 V VOUT Fig. 8.1 (i) Calculate the gain G of the amplifier circuit. G = ...........................................................[2] (ii) Determine the output potential difference VOUT for input potential differences VIN of 1. – 0.10 V, VOUT = ............................................................ V 2. +1.3 V. VOUT = ............................................................ V [2] (iii) The gain of the amplifier shown in Fig. 8.1 is constant. State one change that can be made to the circuit of Fig. 8.1 so that the amplifier circuit monitors light intensity levels, with the magnitude of the gain decreasing as light intensity increases. ........................................................................................................................................... .......................................................................................................................................[1] [Total: 9]

Mark scheme: 8(a)(i) (fraction of) output is combined with the input M1 output (fraction) subtracted/deducted from input A1 8(a)(ii) any two valid points e.g.: • greater bandwidth/gain constant over a larger range of frequencies/greater bandwidth • smaller gain B2 8(b)(i) gain = (–)9600 / 800 C1 = –12 A1 8(b)(ii) 1. 1.2 V B1 2. –6 V B1 8(b)(iii) replace the 9600 Ω resistor with an LDR B1

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9 A rigid copper wire is held horizontally between the pole pieces of two magnets, as shown in Fig. 9.1. 8.5 cm 8.5 cm copper wire S S direction of current θ N N side view top view Fig. 9.1 The width of each pole piece is 8.5 cm. The uniform magnetic flux density B in the region between the poles of the magnets is 3.7 mT and is zero outside this region. The angle between the wire and the direction of the magnetic field is θ. The current in the wire is in the direction shown on Fig. 9.1. (a) By reference to the side view of Fig. 9.1, state and explain the direction of the force on the magnets. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) The constant current in the wire is 5.1 A. (i) For angle θ equal to 90°, calculate the force on the wire. force = ....................................................... N [2] (ii) The angle θ is changed to 60°. 8 .5 The length of wire in the magnetic field is cm. c sin60 ° m Calculate the force on the wire. force = ....................................................... N [1] (c) The constant current in the wire is now changed to an alternating current of frequency 20 Hz and root-mean-square (r.m.s.) value 5.1 A. The angle between the wire and the direction of the magnetic field is 90°. On Fig. 9.2, sketch a graph to show the variation with time t of the force F on the wire for two cycles of the alternating current. F / N 0 0 t / s Fig. 9.2 [3] [Total: 8]

Mark scheme: 9(a) using Fleming’s left-hand rule force on wire is upwards B1 by Newton’s third law, force on magnet is downwards B1 9(b)(i) F = BIL C1 = 3.7 × 10–3 × 5.1 × 8.5 × 10–2 = 1.6 × 10–3 N A1 9(b)(ii) F = 1.6 × 10–3 N A1 9(c) sketch: sinusoidal wave with two cycles B1 amplitude 2.3 × 10–3 N B1 period 0.05 s B1

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10 (a) State Faraday’s law of electromagnetic induction. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) A coil of insulated wire is wound on to one end of a ferrous core and connected to a battery, as shown in Fig. 10.1. ferrous core aluminium ring coil of insulated wire Fig. 10.1 An aluminium ring is placed on the core. The ring can move freely along the length of the core. The switch is initially open. Use Faraday’s law and Lenz’s law to explain why the aluminium ring jumps upwards when the switch is closed. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[4] [Total: 6]

Mark scheme: 10(a) induced e.m.f. proportional to rate M1 of change of (magnetic) flux (linkage) or of cutting (magnetic) flux A1 10(b) current in coil produces flux B1 (by Faraday’s law) changing flux induces e.m.f. in ring B1 current in ring causes field (around ring) B1 (by Lenz’s law) field around ring opposes field around coil B1

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11 (a) (i) Explain what is meant by a photon. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] (ii) By reference to intensity of light, state one piece of evidence provided by the photoelectric effect for a particulate nature of light. ........................................................................................................................................... .......................................................................................................................................[1] (b) Some electron energy levels in a solid are illustrated in Fig. 11.1. conduction band forbidden band valence band Fig. 11.1 A semiconductor material has a very high resistance in darkness. Light incident on the semiconductor material causes its resistance to decrease. Explain the resistance of the semiconductor material in different light conditions. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[5] [Total: 8]

Mark scheme: 11(a)(i) packet/quantum/discrete amount of energy M1 of electromagnetic radiation A1 11(a)(ii) (maximum) energy of emitted electrons is independent of intensity or no emission of electrons below the threshold frequency regardless of intensity or no emission of electrons when photon energy is less than work function (energy) regardless of intensity B1 11(b) in darkness: conduction band empty so high resistance B1 in daylight: electrons in valence band absorb photons B1 in daylight: electrons ‘jump’ to conduction band B1 this leaves holes in valence band B1 more charge carriers in daylight so resistance decreases B1

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12 An X-ray beam is used to produce an image of a model of a thumb. A parallel beam of X-ray radiation of intensity I0 is incident on the model, as illustrated in Fig. 12.1. soft tissue bone incident beam 1.3 cm emergent beam intensity I0 2.8 cm Fig. 12.1 Data for the attenuation (absorption) coefficient μ in bone and in soft tissue are shown in Fig. 12.2. μ/ cm–1 bone 3.0 soft tissue 0.90 Fig. 12.2 (a) Calculate, in terms of the incident intensity I0 of the X-ray beam, the intensity of the beam after passing through (i) a thickness of 2.8 cm of soft tissue, intensity = ...................................................... I0 [2] (ii) the bone and soft tissue, as shown in Fig. 12.1. intensity = ...................................................... I0 [2] (b) (i) State what is meant by the contrast of an X-ray image. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] (ii) By reference to your answers in (a), suggest whether the X-ray image of the model has good contrast. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[1] [Total: 7]

Mark scheme: 12(a)(i) C1 = I0 exp (–0.90 × 2.8) = 0.080 I0 A1 12(a)(ii) I = I0 exp [(–0.90 × 1.5) × (–3.0 × 1.3)] C1 = I0 (0.259 × 0.20) = 0.0052 I0 A1 12(b)(i) difference in degrees of blackening M1 between structures A1 12(b)(ii) large difference in intensities so good contrast B1

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13 (a) State what is meant by radioactive decay. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) The variation with time t of the number N of technetium-101 nuclei in a sample of radioactive material is shown in Fig. 13.1. 10.0 8.0 N / 107 6.0 4.0 2.0 0 0 10 20 30 40 t / min Fig. 13.1 (i) Use Fig. 13.1 to determine the activity, in Bq, of the sample of technetium-101 at time t = 14.0 minutes. Show your working. activity = ..................................................... Bq [4] (ii) Without calculating the half-life of technetium-101, use your answer in (i) to determine the decay constant λ of technetium-101. λ = .................................................... s–1 [2] [Total: 8]

Mark scheme: 13(a) emission of particles/radiation by unstable nucleus B1 spontaneous emission B1 13(b)(i) use of graph to determine half-life = 14 minutes B1 hence λ = ln 2 / (14 × 60) (s–1) C1 N at 14 minutes = 4.4 × 107 and A = λN C1 activity = 4.4 × 107 × ln 2 / (14 × 60) = 3.6 × 104 Bq A1 or correct tangent drawn at time t = 14 minutes (B1) magnitude of gradient of tangent identified as activity (C1) correct working for gradient leading to activity (C1) activity = 3.6 × 104 Bq (A1) 13(b)(ii) 3.6 × 104 = λ × 4.4 × 107 or λ = ln 2 / (14.0 × 60) C1 λ = 8.2 × 10–4 s–1 A1

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