Cambridge A Level Physics 9702 — 2009 Oct/Nov Paper 4 · Variant 1

1 (a) State Newton’s law of gravitation. .......................................................................................................................................... .......................................................................................................................................... .................................................................................................................................... [2] (b) The Earth may be considered to be a uniform sphere of radius R equal to 6.4 × 106 m. A satellite is in a geostationary orbit. (i) Describe what is meant by a geostationary orbit. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [3] (ii) Show that the radius x of the geostationary orbit is given by the expression gR2 = x3ω2 where g is the acceleration of free fall at the Earth’s surface and ω is the angular speed of the satellite about the centre of the Earth. [3] (iii) Determine the radius x of the geostationary orbit. radius = ........................................... m [3]

Mark scheme: 1 (a) F ∝ Mm / R2 …..…(words or explained symbols) ................................................M1 either M and m are point masses or R >> diameter of masses …(do not allow ‘size’) ....................................... A1 [2] (b) (i) equatorial orbit .................................................................................................... B1 period 24 hours / same angular speed ............................................................... B1 from west to east / same direction of rotation ..................................................... B1 [3] (allow one of the last two marks for ‘always overhead’ if 2nd or 3rd marks not scored) (ii) gravitational force provides centripetal force / gives rise to centripetal acceleration ….(in ‘words’) ........................................ B1 GM / x2 = xω2 ....................................................................................................M1 g = GM / R2 .......................................................................................................M1 to give gR2 = x3ω2 ............................................................................................ A0 [3] (iii) ω = 2π / (24 × 3600) = 7.27 × 10-5 rad s-1 ........................................................C1 9.81 × (6.4 × 106)2 = x3 × (7.27 × 10-5)2 .............................................................C1 x3 = 7.6 × 1022 x = 4.2 × 107 m ................................................................................................. A1 [3] (use of g = 10 m s-2, loses 1 mark but once only in the Paper) [Total: 11]

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2 An ideal gas occupies a container of volume 4.5 × 103 cm3 at a pressure of 2.5 × 105 Pa and For a temperature of 290 K. Examiner’s Use (a) Show that the number of atoms of gas in the container is 2.8 × 1023. [2] (b) Atoms of a real gas each have a diameter of 1.2 × 10–10 m. (i) Estimate the volume occupied by 2.8 × 1023 atoms of this gas. volume = ......................................... m3 [2] (ii) By reference to your answer in (i), suggest whether the real gas does approximate to an ideal gas. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [2]

Mark scheme: 2 (a) either pV = NkT or pV = nRT and n = N / NA .....................................................C1 clear correct substitution e.g. 2.5 × 105 × 4.5 × 103 × 10-6 = N × 1.38 × 10-23 × 290 ...............................................M1 N = 2.8 × 1023 .......................................................................................................... A0 [2] (allow 1 mark for calculation of n = 0.467 mol) 4 (b) (i) volume = (1.2 × 10-10)3 × 2.8 × 1023 or πr3 × 2.8 × 1023 ..............................C1 3 = 4.8 × 10-7 m3 2.53 × 10-7 m3 ..................................... A1 [2] (ii) either 4.5 × 103 cm3 >> 0.48 cm3 or ratio of volumes is about 10-4 ................ B1 justified because volume of molecules is negligible ........................................... B1 [2] [Total: 6] GCE A/AS LEVEL – October/November 2009 9702 41

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3 (a) A student states, quite wrongly, that temperature measures the amount of thermal For energy (heat) in a body. Examiner’s Use State and explain two observations that show why this statement is incorrect. 1. ..................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... 2. ..................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... [4] (b) A thermometer and an electrical heater are inserted into holes in an aluminium block of mass 960 g, as shown in Fig. 3.1. connections to thermometer electrical circuit aluminium block Fig. 3.1 The power rating of the heater is 54 W. For Examiner’s The heater is switched on and readings of the temperature of the block are taken at Use regular time intervals. When the block reaches a constant temperature, the heater is switched off and then further temperature readings are taken. The variation with time t of the temperature θ of the block is shown in Fig. 3.2. θ 0 t Fig. 3.2 (i) Suggest why the rate of rise of temperature of the block decreases to zero. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [2] (ii) After the heater has been switched off, the maximum rate of fall of temperature is 3.7 K per minute. Estimate the specific heat capacity of aluminium. specific heat capacity = .............................. J kg–1 K–1 [3]

Mark scheme: 3 (a) e.g. two objects of different masses at same temperature (M1) same material would have different amount of heat (A1) e.g. temperature shows direction of heat transfer (M1) from high to low regardless of objects (A1) e.g. when substance melts/boils (M1) heat input but no temperature change (A1) any two, M1 + A1 each, max 4 ………………………………..…………........................... [4] (b) (i) energy losses (to the surroundings) .................................................................M1 either increase as the temperature rises or rise is zero when heat loss = heat input ............................................... A1 [2] (ii) idea of input power = maximum rate of heat loss .............................................C1 power = m × c × ∆θ / ∆t 54 = 0.96 × c × 3.7 / 60 .....................................................................................C1 c = 910 J kg-1 K-1 ............................................................................................... A1 [3] [Total: 9]

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4 The variation with time t of the displacement x of the cone of a loudspeaker is shown in For Fig. 4.1. Examiner’s Use 0.3 x / mm 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 t / ms – 0.1 – 0.2 – 0.3 Fig. 4.1 (a) Use Fig. 4.1 to determine, for these oscillations, (i) the amplitude, amplitude = ........................................ mm [1] (ii) the frequency. frequency = .......................................... Hz [2] (b) State two times at which (i) the speed of the cone is maximum, time ............................... ms and time ............................... ms [1] (ii) the acceleration of the cone is maximum. time ............................... ms and time ............................... ms [1] (c) The effective mass of the cone is 2.5 g. For Examiner’s Use your answers in (a) to determine the maximum kinetic energy of the cone. Use kinetic energy = ............................................ J [3] (d) The loudspeaker must be designed so that resonance of the cone is avoided. (i) State what is meant by resonance. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [2] (ii) State and briefly explain one other situation in which resonance should be avoided. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ................................................................................................................. [2]

Mark scheme: 4 (a) (i) amplitude = 0.2 mm .......................................................................................... A1 [1] (ii) period = 1.2 ms .................................................................................................C1 frequency = 830 Hz .......................................................................................... A1 [2] (b) (i) any two of zero, 0.6 ms and 1.2 ms .................................................................... A1 [1] (ii) any two of 0.3 ms, 0.9 ms, 1.5 ms ...................................................................... A1 [1] (c) either v = ωx0 = 2πfx0 = 2π × 830 × 0.2 × 10-3 = 1.05 m s-1 or slope of graph = 1.0 m s-1 ……(allow ± 0.1 m s-1) .......................................C1 EK = ½mv2 = ½ × 2.5 × 10-3 × 1.052 .....................................................................................C1 = 1.4 × 10-3 J ...................................................................................................... A1 [3] (d) (i) large / maximum amplitude of vibration .............................................................. B1 when impressed frequency equals natural frequency of vibration ...................... B1 [2] (ii) e.g. metal panels on machinery vibrate / oscillate ........................................... (M1) motor in machine impresses frequency on panel ......................................(A1) e.g. car suspension system vibrates / oscillates................................................. (M1) going over bumps would give large amplitude vibrations.............................(A1) any feasible example, M1 + A1 ............................................................................... [2] [Total: 12] GCE A/AS LEVEL – October/November 2009 9702 41

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5 (a) Define electric potential at a point. For Examiner’s .......................................................................................................................................... Use .......................................................................................................................................... .................................................................................................................................... [2] (b) An α-particle is emitted from a radioactive source with kinetic energy of 4.8 MeV. The α-particle travels in a vacuum directly towards a gold (19779Au) nucleus, as illustrated in Fig. 5.1. path of gold α - particle nucleus Fig. 5.1 The α-particle and the gold nucleus may be considered to be point charges in an isolated system. (i) Explain why, as the α-particle approaches the gold nucleus, it comes to rest. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [2] (ii) For the closest approach of the α-particle to the gold nucleus determine 1. their separation, separation = ........................................... m [3] 2. the magnitude of the force on the α-particle. For Examiner’s Use force = .......................................... N [2]

Mark scheme: 5 (a) work done per / on unit positive charge .....................................................................M1 moving charge from infinity to the point ..................................................................... A1 [2] (b) (i) α-particle and gold nucleus repel each other ..................................................... B1 all kinetic energy of α-particle converted into electric potential energy .............. B1 [2] (ii) 1 potential energy = (79 × 2 × {1.6 × 10-19}2) / (4π × 8.85 × 10-12 × d) ..............C1 kinetic energy = 4.8 × 1.6 × 10-13 = 7.68 × 10-13 J ...........................................C1 equating to give d = 4.7 × 10-14 m ..................................................................... A1 [3] (ii) 2 F = Qq / 4πε0d × 1 / d = 7.68 × 10-13 × 1 / (4.7 × 10-14) ..............................C1 = 16 N ....................................................................................................... A1 [2] [Total: 9]

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6 The current in a long, straight vertical wire is in the direction XY, as shown in Fig. 6.1. For Examiner’s Y Use D C A B X Fig. 6.1 (a) On Fig. 6.1, sketch the pattern of the magnetic flux in the horizontal plane ABCD due to the current-carrying wire. Draw at least four flux lines. [3] (b) The current-carrying wire is within the Earth’s magnetic field. As a result, the pattern drawn in Fig. 6.1 is superposed with the horizontal component of the Earth’s magnetic field. Fig. 6.2 shows a plan view of the plane ABCD with the current in the wire coming out of the plane. D C magnetic field current out of of Earth plane ABCD A B Fig. 6.2 The horizontal component of the Earth’s magnetic field is also shown. (i) On Fig. 6.2, mark with the letter P a point where the magnetic field due to the For current-carrying wire could be equal and opposite to that of the Earth. [1] Examiner’s Use (ii) For a long, straight wire carrying current I, the magnetic flux density B at distance r from the centre of the wire is given by the expression I B = μ0 2πr where μ0 is the permeability of free space. The point P in (i) is found to be 1.9 cm from the centre of the wire for a current of 1.7 A. Calculate a value for the horizontal component of the Earth’s magnetic flux density. flux density = ............................................ T [2] (c) The current in the wire in (b)(ii) is increased. The point P is now found to be 2.8 cm from the wire. Determine the new current in the wire. current = ............................................ A [2]

Mark scheme: 6 (a) concentric circles …(at least three lines) ................................................................M1 with increasing separation ......................................................................................... A1 correct direction clear ................................................................................................ B1 [3] (b) (i) correct position to left of wire .............................................................................. B1 [1] (ii) B = (4π × 10-7 × 1.7) / (2π × 1.9 × 10-2) .............................................................C1 = 1.8 × 10-5 T ................................................................................................. A1 [2] (c) distance ∝ current ...................................................................................................C1 current = (2.8 / 1.9) × 1.7 = 2.5 A ........................................................................................................ A1 [2] [Total: 8]

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7 A sinusoidal alternating voltage is to be rectified. For Examiner’s (a) Suggest one advantage of full-wave rectification as compared with half-wave Use rectification. .......................................................................................................................................... .................................................................................................................................... [1] (b) The rectification is produced using the circuit of Fig. 7.1. A R B Fig. 7.1 All the diodes may be considered to be ideal. The variation with time t of the alternating voltage applied to the circuit is shown in Fig. 7.2 and in Fig. 7.3. voltage 00 t Fig. 7.2 voltage 00 t Fig. 7.3 (i) On the axes of Fig. 7.2, draw a graph to show the variation with time t of the potential For difference across diode A. [1] Examiner’s Use (ii) On the axes of Fig. 7.3, draw a graph to show the variation with time t of the potential difference across diode B. [1] (c) (i) On Fig. 7.1, draw the symbol for a capacitor, connected into the circuit so as to provide smoothing. [1] (ii) Fig. 7.4 shows the variation with time t of the smoothed potential difference across the resistor R in Fig. 7.1. potential difference t Fig. 7.4 1. State how the amount of smoothing may be increased. .................................................................................................................................. ............................................................................................................................ [1] 2. On Fig. 7.4, draw the variation with time t of the potential difference across resistor R for increased smoothing. [2]

Mark scheme: 7 (a) e.g. more (output) power available e.g. less ripple for same smoothing capacitor any sensible suggestion ............................................................................................ B1 [1] (b) (i) curve showing half-wave rectification ................................................................. B1 [1] (ii) similar to (i) but phase shift of 180° .................................................................... B1 [1] (c) (i) correct symbol, connected in parallel with R ...................................................... B1 [1] (ii) 1 larger capacitor / second capacitor in parallel with R ..................................... B1 [1] (not increase R) 2 same peak values ........................................................................................... B1 correct shape giving less ripple .......................................................................... B1 [2] [Total: 7] GCE A/AS LEVEL – October/November 2009 9702 41

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8 The controlled reaction between deuterium (2 H) and tritium (3 H) has involved ongoing 1 1 For research for many years. The reaction may be summarised as Examiner’s Use 2 H + 3 H 4 + 1 n + Q 1 1 2He 0 where Q = 17.7 MeV. Binding energies per nucleon are shown in Fig. 8.1. binding energy per nucleon / MeV 2 H 1.12 1 1 n – 0 42He 7.07 Fig. 8.1 (a) Suggest why binding energy per nucleon for the neutron is not quoted. .......................................................................................................................................... .................................................................................................................................... [1] (b) Calculate the mass defect, in kg, of a helium 42He nucleus. mass defect = .......................................... kg [3] (c) (i) State the name of the type of reaction illustrated by this nuclear equation. ............................................................................................................................ [1] (ii) Determine the binding energy per nucleon, in MeV, of tritium (3 H). 1 binding energy per nucleon = ....................................... MeV [3]

Mark scheme: 8 (a) neutron is a single nucleon / particle ......................................................................... B1 [1] (b) binding energy = 4 × 7.07 × 1.6 × 10-13 ....................................................................C1 = 4.52 × 10-12 J binding energy = c2 ∆m ...........................................................................................C1 4.52 × 10-12 = (3.0 × 108)2 × ∆m ∆m = 5.03 × 10-29 kg ................................................................................................ A1 [3] (c) (i) fusion ……(do not allow fussion) .................................................................... B1 [1] (ii) (2 × 1.12) + 3x = 28.28 ...................................................................................C1 …... –17.7 ..........................................................................................................C1 x = 2.78 MeV per nucleon ................................................................................ A1 [3] (use of +17.7 gives x = 14.6 MeV, allow 1 mark only) [Total: 8] GCE A/AS LEVEL – October/November 2009 9702 41 Section B

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9 A metal wire strain gauge is firmly fixed across a crack in a wall, as shown in Fig. 9.1, so that the growth of the crack may be monitored. strain crack gauge Fig. 9.1 (a) Explain why, as the crack becomes wider, the resistance of the strain gauge increases. .......................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... .................................................................................................................................... [3] (b) The strain gauge has an initial resistance of 143.0 Ω and, after being fixed in position across the crack for several weeks, the resistance is found to be 146.2 Ω. The change in the area of cross-section of the strain gauge wire is negligible. Calculate the percentage increase in the width of the crack. Explain your working. increase = ........................................... % [3]

Mark scheme: 9 (a) resistance of wire = ρL / A ....................................................................................... B1 as crack widens, L increases ....................................................................................M1 and A decreases ............................................................................M1 so resistance increases ............................................................................................. A0 [3] (b) ∆L / L = ∆R / R ........................................................................................................ B1 = (146.2 – 143.0) / 143.0 × 100 ..................................................................C1 ∆L / L = 2.24% ......................................................................................................... A1 [3] [Total: 6]

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10 The circuit of Fig. 10.1 may be used to indicate temperature change. For Examiner’s Use +2 V T P +5V – + –5V R G P P Fig. 10.1 The resistance of the thermistor T at 16 °C is 2100 Ω and at 18 °C, the resistance is 1900 Ω. Each resistor P has a resistance of 2000 Ω. Determine the change in the states of the light-emitting diodes R and G as the temperature of the thermistor changes from 16 °C to 18 °C. ................................................................................................................................................. ........................................................................................................................................... [4]

Mark scheme: 10 at 16 °C, V+ = 1.00 V and V – = 0.98 V or V+ > V – ........................................................ B1 at 16 °C, output is positive ................................................................................................M1 diode R is ‘on’ and diode G is ‘off’ .................................................................................... A1 as temperature rises, diode R goes ‘off’ and diode G goes ‘on’ ....................................... B1 [4] (allow e.c.f. from 2nd to 3rd marks and also 3rd to 4th marks) [Total: 4]

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11 Outline briefly the main principles of the use of magnetic resonance to obtain diagnostic For information about internal body structures. Examiner’s Use ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ................................................................................................................................................. ........................................................................................................................................... [6]

Mark scheme: 11 large / 1 T magnetic field applied along body (allow ‘across’) (1) r.f. pulse applied ............................................................................................................... (1) causes hydrogen nuclei / protons ..................................................................................... (1) to resonate ....................................................................................................................... (1) (nuclei) return to equilibrium state / after relaxation time ................................................. (1) r.f. (pulse) emitted ............................................................................................................ (1) pulses detected, processed and displayed ...................................................................... (1) resonant frequency depends on magnetic field strength .................................................. (1) calibrated non-uniform field enables nuclei to be located ................................................ (1) any six points, one mark each .......................................................................................... B6 [6] [Total: 6] GCE A/AS LEVEL – October/November 2009 9702 41

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12 (a) State and explain two advantages of the transmission of information in digital, rather For than analogue, form. Examiner’s Use 1. ..................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... [4] (b) Convert (i) the decimal number 13 to a four-bit digital number, ............................................................................................................................ [1] (ii) the digital number 0101 to a decimal number. ............................................................................................................................ [1] (c) An analogue signal is to be transmitted digitally. A block diagram for part of the transmission system is shown in Fig. 12.1. block X block Y parallel analogue to transmission recovered ADC signal serial analogue converter signal Fig. 12.1 (i) Complete Fig. 12.1 by labelling block X and block Y. [2] (ii) State the purpose of the parallel-to-serial converter. .................................................................................................................................. .................................................................................................................................. ............................................................................................................................ [2] (d) The original analogue signal is shown in Fig. 12.2. The recovered signal after transmission For is shown in Fig. 12.3. Examiner’s Use signal recovered signal 00 time 00 time Fig. 12.2 Fig. 12.3 Suggest and explain two ways in which the reproduction of the input signal may be improved. 1. ...................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... 2. ...................................................................................................................................... .......................................................................................................................................... .......................................................................................................................................... [4]

Mark scheme: 12 (a) e.g. signal can be regenerated .................................................................................M1 so that there is minimal noise .................................................................................... A1 e.g. extra data can be added ....................................................................................M1 so that signal can be checked for errors .................................................................... A1 [4] (any two, sensible suggestions, M1 + A1, max 4) (b) (i) 1101 ................................................................................................................... B1 [1] (ii) 5 ......................................................................................................................... B1 [1] (c) (i) block X: serial-to parallel ................................................................................... B1 block Y: DAC / digital-to-analogue (converter) .................................................. B1 [2] (ii) takes the simultaneous / all bits of a number ....................................................M1 and transmits them one after another / down a single line ................................ A1 [2] (d) increase number of bits in digital number at each sampling ......................................M1 so that step height is reduced ................................................................................... A1 increase sampling frequency / reduce time between samples ..................................M1 so that depth / width of step is reduced ..................................................................... A1 [4] (do not allow ‘smoother output’) [Total: 14]

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