Cambridge A Level Physics 9702 — 2015 Oct/Nov Paper 4 · Variant 1

1 A satellite of mass mS is in a circular orbit of radius x about the Earth. The Earth may be considered to be an isolated uniform sphere with its mass M concentrated at its centre. (a) (i) Show that the kinetic energy EK of the satellite is given by the expression GMmS EK = 2x where G is the gravitational constant. Explain your working. [3] (ii) State an expression, in terms of G, M, mS and x, for the potential energy EP of the satellite. .......................................................................................................................................[1] (iii) Using answers from (i) and (ii), derive an expression for the total energy ET of the satellite. ET = ...........................................................[2] (b) Small resistive forces acting on the satellite cause the radius of its circular orbit to change. Use your answers in (a) to state, for the satellite, whether each of the following quantities increases, decreases or remains constant. (i) total energy .......................................................................................................................................[1] (ii) radius of orbit .......................................................................................................................................[1] (iii) potential energy .......................................................................................................................................[1] (iv) kinetic energy .......................................................................................................................................[1]

Mark scheme: 1 (a) (i) gravitational force provides/is the centripetal force B1 GMmS / x2 = mSv2 / x (allow x or r; allow m or mS) M1 EK = ½mSv2 and clear algebra leading to EK = GMmS / 2x A1 [3] (ii) EP = – GMmS / x (sign essential) B1 [1] (iii) ET = EK + EP = GMmS / 2x – GMmS / x C1 = – GMmS / 2x (allow ECF from (a)(ii)) A1 [2] (b) (i) decreases B1 [1] (ii) decreases B1 [1] (iii) decreases B1 [1] (iv) increases B1 [1] (for answers in (b) allow ECF from (a)(iii))

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2 (a) State what is meant by an ideal gas. ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) The mean-square speed of the atoms of a fixed mass of an ideal gas at 32 °C is 1.9 × 106 m2 s–2. The gas is heated at constant volume to a temperature of 80 °C. Determine (i) the rise, in kelvin, of the temperature of the gas, temperature rise = ...................................................... K [1] (ii) the root-mean-square (r.m.s.) speed of the atoms at 80 °C. r.m.s. speed = ................................................ m s–1 [3]

Mark scheme: 2 (a) obeys the equation pV = nRT or pV / T = constant M1 all symbols explained; T in kelvin/thermodynamic temperature A1 [2] (b) (i) temperature rise = 48 K A1 [1] (ii) <c2> ∝ T or equivalent C1 <c2> = (353 / 305) × 1.9 × 106 C1 cr.m.s. = 1480 m s–1 A1 [3]

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3 (a) State an expression, in terms of work done and heating, that is used to calculate the increase in internal energy of a system. ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) State and explain, in terms of your expression in (a), the change, if any, in the internal energy (i) of the water in an ice cube when the ice melts, at atmospheric pressure, to form a liquid without any change of temperature, ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[3] (ii) of the gas in a tyre when the tyre bursts so that the gas suddenly increases in volume. Assume that the gas is ideal. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[3]

Mark scheme: 3 (a) heat/thermal energy gained by system or energy transferred to system by heating B1 plus work done on the system or minus work done by the system B1 [2] (b) (i) either volume decreases so work done on the system or small volume change so work done on system negligible M1 (thermal) energy absorbed to break lattice structure M1 internal energy increases A1 [3] (ii) gas expands so work done by gas (against atmosphere) M1 no time for thermal energy to enter or leave the gas M1 internal energy decreases A1 [3]

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4 (a) Distinguish between free oscillations and forced oscillations. free oscillations: ........................................................................................................................ ................................................................................................................................................... forced oscillations: .................................................................................................................... ................................................................................................................................................... [2] (b) A trolley is held on a horizontal surface by means of two stretched springs, as shown in Fig. 4.1. spring trolley spring fixed point oscillator Fig. 4.1 One spring is attached to a fixed point. The other spring is attached to an oscillator that causes horizontal oscillations of the trolley. The oscillator vibrates with a constant amplitude of vibration. The frequency of vibration of the oscillator is gradually increased from a very low value. The variation with frequency f of the amplitude x0 of vibration of the trolley is shown in Fig. 4.2. x0 1.5 2.0 2.5 3.0 f / Hz Fig. 4.2 Use Fig. 4.2 to state and explain (i) the value of the natural frequency of vibration of the trolley, ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[3] (ii) whether there are any frictional forces acting on the trolley. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[1] (c) The oscillator in (b) is now stopped. The trolley is given a horizontal displacement of 4.7 cm along the line of the springs. The trolley is then released. Use information from Fig. 4.2 to estimate the maximum speed of the trolley. speed = ................................................ m s–1 [2]

Mark scheme: 4 (a) free: (body oscillates) without any loss of energy/no resistive forces/no external forces applied B1 forced: continuous energy input (required)/body is made to vibrate by an (external) periodic force/driving oscillator B1 [2] (b) (i) idea of resonance B1 maximum amplitude at natural frequency B1 frequency = 2.1 Hz (allow 2.08 to 2.12 Hz) B1 [3] (ii) peak not very sharp/amplitude not infinite so frictional forces are present B1 [1] (c) v = ωx0 = 2π × 2.1 × 4.7 × 10–2 (allow ECF from (b)(i)) C1 = 0.62 m s–1 A1 [2]

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5 A charged particle P is situated in a vacuum at a distance x from the centre of a charged conducting sphere of radius r, as illustrated in Fig. 5.1. P r x Fig. 5.1 For the particle P outside the conducting sphere, the charge on the sphere may be assumed to be a point charge at its centre. (a) (i) State Coulomb’s law. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] (ii) The sphere and the particle P are both charged positively. 1. State the direction of the force acting on particle P. .......................................................................................................................................[1] 2. State the position of particle P for the force to be maximum. .......................................................................................................................................[1] 3. Determine the ratio force on particle P at x = r . force on particle P at x = 4r ratio = .......................................................... [2] (b) When the charge on the sphere is 6.0 × 10–7 C, the electric field strength at the surface of the sphere is 1.5 × 106 V m–1. Electrical breakdown (a spark) occurs when the electric field strength at the surface of the sphere exceeds 2.0 × 106 V m–1. Determine the additional charge that may be added to the sphere before breakdown occurs. charge = ...................................................... C [3]

Mark scheme: 5 (a) (i) force proportional to the product of the two/point charges B1 and inversely proportional to the square of their separation B1 [2] (ii) 1. force radially away from sphere/to right/to east B1 [1] 2. (maximum) at/on surface of sphere or x = r B1 [1] 3. F ∝ 1 / x2 or F = q1q2 / (4πε 0x2) C1 ratio = 16 A1 [2] (b) E = q / (4πε0x2) or E ∝ q C1 maximum charge = (2.0 / 1.5) × 6.0 × 10–7 C1 = 8.0 × 10–7 C additional charge = 2.0 × 10–7 C A1 [3]

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6 (a) A particle has mass m, charge +q and speed v. State the magnitude and direction of the force, if any, on the particle when the particle is travelling along the direction of (i) a uniform gravitational field of field strength g, ........................................................................................................................................... .......................................................................................................................................[2] (ii) a uniform magnetic field of flux density B. ........................................................................................................................................... .......................................................................................................................................[1] (b) Two charged horizontal metal plates, situated in a vacuum, produce a uniform electric field of field strength E between the plates. The field strength outside the region between the plates is zero. The particle in (a) enters the region of the electric field at right-angles to the direction of the field, as illustrated in Fig. 6.1. particle, v charge +q mass m E Fig. 6.1 A uniform magnetic field is to be applied in the same region as the electric field so that the particle passes undeviated through the region between the plates. (i) State and explain the direction of the magnetic field. ........................................................................................................................................... .......................................................................................................................................[2] (ii) Derive, with explanation, the relation between the speed v and the magnitudes of the electric field strength E and the magnetic flux density B. [3] (c) A second particle has the same mass m and charge +q as that in (b) but its speed is 2v. This particle enters the region between the plates along the same direction as the particle in (b). On Fig. 6.1, sketch the path of this particle in the region between the plates. [2]

Mark scheme: 6 (a) (i) force = mg M1 along the direction of the field/of the motion A1 [2] (ii) no force B1 [1] (b) (i) force due to E-field downwards so force due to B-field upwards B1 into the plane of the paper B1 [2] (ii) force due to magnetic field = Bqv B1 force due to electric field = Eq B1 (use of FB and FE not explained, allow 1/2) forces are equal (and opposite) so Bv = E or Eq = Bqv so E = Bv B1 [3] (c) sketch: smooth curved path M1 in ‘upward’ direction A1 [2]

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7 (a) By reference to the photoelectric effect, state what is meant by the threshold frequency. ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) Electrons are emitted from a metal surface when light of a particular wavelength is incident on the surface. Explain why the emitted electrons have a range of values of kinetic energy below a maximum value. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (c) The wavelength of the incident radiation is λ. The variation with 1/λ of the maximum kinetic energy EMAX of electrons emitted from a metal surface is shown in Fig. 7.1. 4.0 3.0 EMAX / 10–19 J 2.0 1.0 0 1.0 1.5 2.0 2.5 3.0 3.5 1 – / 106 m–1 h Fig. 7.1 (i) Use Fig. 7.1 to determine, without reference to the work function energy, the threshold frequency f0. f0 = .................................................... Hz [2] (ii) Use your answer in (i) to calculate the work function energy Φ. Φ = ....................................................... J [2] (d) Caesium metal has a work function energy of 2.2 × 10–19 J. On the axes of Fig. 7.1, sketch a graph to show the variation with 1/λ of EMAX for caesium metal. [2]

Mark scheme: 7 (a) minimum frequency of e.m. radiation/a photon (not “light”) M1 for emission of electrons from a surface A1 [2] (reference to light/UV rather than e.m. radiation, allow 1/2) (b) EMAX corresponds to electron emitted from surface B1 electron (below surface) requires energy to bring it to surface, so less than EMAX B1 [2] (c) (i) 1/λ0 = 1.85 × 106 (allow 1.82 to 1.88) C1 f0 = c / λ0 = 3.00 × 108 × 1.85 × 106 = 5.55 × 1014 Hz A1 [2] (ii) Φ = hf0 = 6.63 × 10–34 × 5.55 × 1014 (allow ECF from (c)(i)) C1 = 3.68 × 10–19 J A1 [2] (d) sketch: straight line with same gradient M1 intercept between 1.0 and 1.5 A1 [2]

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8 (a) Distinguish, for an atom, between a nucleus and a nucleon. nucleus: ..................................................................................................................................... ................................................................................................................................................... nucleon: .................................................................................................................................... ................................................................................................................................................... [3] (b) Radon gas is a naturally occurring radioactive gas with a half-life of 3.8 days. The activity of radon gas in a room is found to be 97 Bq in each 1.0 m3 of air. (i) Calculate 1. the decay constant, in s–1, of radon, decay constant = .................................................... s–1 [2] 2. the number of radon atoms giving rise to an activity of 97 Bq. number = .......................................................... [2] (ii) A volume of 2.5 × 10–2 m3 of air in the room contains 1.0 mol of molecules. Determine the ratio, for 1.0 m3 of air, number of radon atoms . number of air molecules ratio = .......................................................... [2]

Mark scheme: 8 (a) nucleus: small central part/core of an atom B1 nucleon: proton or a neutron B1 particle contained within a nucleus B1 [3] (b) (i) 1. decay constant = ln 2 / (3.8 × 24 × 3600) C1 = 2.1 × 10–6 s–1 A1 [2] 2. A = λN 97 = 2.1 × 10–6 × N C1 N = 4.6 × 107 A1 [2] (ii) 1.0 m3 contains (6.02 × 1023) / (2.5 × 10–2) air molecules C1 ratio = (4.6 × 107 × 2.5 × 10–2) / (6.02 × 1023) = 1.9 × 10–18 A1 [2] Section B

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9 A battery of e.m.f. 6.0 V and negligible internal resistance is connected to three resistors, each of resistance 2.0 kΩ, and a thermistor, as shown in Fig. 9.1. 2.0 k1 6.0 V A B 2.0 k1 2.0 k1 Fig. 9.1 The thermistor has resistance 2.8 kΩ at 10 °C and resistance 1.8 kΩ at 20 °C. (a) Calculate the potential (i) at point A, potential = ...................................................... V [1] (ii) at point B for the thermistor at 10 °C, potential = ...................................................... V [2] (iii) at point B for the thermistor at 20 °C. potential = ...................................................... V [1] (b) The points A and B in Fig. 9.1 are connected to the inputs of an ideal operational amplifier (op-amp), as shown in Fig. 9.2. +9 V A – B + VOUT –9 V Fig. 9.2 The thermistor is warmed from 10 °C to 20 °C. State and explain the change in the output potential VOUT of the op-amp as the thermistor is warmed. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[4]

Mark scheme: 9 (a) (i) (+) 3.0 V B1 [1] (ii) potential = 6.0 × {2.0 / (2.0 + 2.8)} C1 = 2.5 V A1 [2] (iii) potential = 6.0 × {2.0 / (2.0 + 1.8)} = 3.2 V A1 [1] (b) at 10 °C, VA > VB M1 VOUT is –9.0 V (allow “negative saturation”) A1 at 20 °C, VOUT is +9.0 V B1 (if 20 °C considered initially, mark as M1,A1,B1) sudden switch (from –9 V to +9 V) when VA = VB B1 [4]

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10 (a) Explain what is meant by the sharpness and by the contrast of an X-ray image. sharpness: ................................................................................................................................ ................................................................................................................................................... contrast: .................................................................................................................................... ................................................................................................................................................... [2] (b) A parallel X-ray beam of intensity I is incident on a medium of thickness x, as illustrated in Fig. 10.1. x incident transmitted intensity I intensity IT medium Fig. 10.1 The transmitted intensity is IT. Data for the linear absorption (attenuation) coefficient μ for 80 keV X-rays in bone and in muscle are given in Fig. 10.2. μ/ cm–1 bone 3.0 muscle 0.27 Fig. 10.2 (i) State, with reference to the production of X-rays, what is meant by 80 keV X-rays. ........................................................................................................................................... ........................................................................................................................................... .......................................................................................................................................[2] (ii) Calculate the ratio IT / I for 80 keV X-rays passing through a thickness of 1.4 cm of bone. ratio = .......................................................... [2] (c) An X-ray image of the upper leg of a student is produced. Part of the X-ray beam passes through a comparatively large thickness of muscle and part through some muscle and the leg bone. Use data from Fig. 10.2 to suggest whether the image has good contrast. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[3]

Mark scheme: 10 (a) sharpness: clarity of edges/resolution (of image) B1 contrast: difference in degree of blackening (of structures) B1 [2] (b) (i) X-rays produced when (high speed) electrons hit target/anode B1 either electrons have been accelerated through 80 kV or electrons have (kinetic) energy of 80 keV B1 [2] (ii) IT / I = e–3.0 × 1.4 C1 = 0.015 A1 [2] (c) for good contrast, µx or eµx or e–µx must be very different B1 µx or eµx or e–µx for bone and muscle will be different than that for muscle M1 so good contrast A1 [3]

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11 A carrier wave is frequency modulated. (a) Describe what is meant by frequency modulation. ................................................................................................................................................... ................................................................................................................................................... ...............................................................................................................................................[2] (b) The sinusoidal carrier wave has a frequency of 750 kHz and an amplitude of 5.0 V. The carrier wave is frequency modulated by a sinusoidal signal of frequency 7.5 kHz and amplitude 1.5 V. The frequency deviation of the carrier wave is 20 kHz V–1. Determine, for the frequency-modulated carrier wave, (i) the amplitude, amplitude = ...................................................... V [1] (ii) the minimum frequency, minimum frequency = .................................................. kHz [1] (iii) the maximum frequency, maximum frequency = .................................................. kHz [1] (iv) the number of times per second that the frequency changes from its minimum value to its maximum value and then back to the minimum value. number = .................................................... s–1 [1]

Mark scheme: 11 (a) frequency of carrier wave varies M1 in synchrony with the displacement of the signal/information wave A1 [2] (b) (i) 5.0 V A1 [1] (ii) 720 kHz A1 [1] (iii) 780 kHz A1 [1] (iv) 7500 A1 [1]

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12 (a) When infra-red radiation passes along an optic fibre, it is attenuated. (i) State what is meant by attenuation. ........................................................................................................................................... .......................................................................................................................................[1] (ii) The infra-red radiation is transmitted as a series of pulses. State and explain two advantages of the digital, rather than the analogue, transmission of information. 1. ........................................................................................................................................ ........................................................................................................................................... ........................................................................................................................................... 2. ........................................................................................................................................ ........................................................................................................................................... ........................................................................................................................................... [4] (b) The input light power to an optic fibre of length 36 km is 145 mW. The output light power is 29 mW. Calculate, in dB km–1, the attenuation per unit length of the optic fibre. attenuation per unit length = .............................................dB km–1 [2]

Mark scheme: 12 (a) (i) (gradual) loss of power/intensity/amplitude (not “signal”) B1 [1] (ii) e.g. noise can be eliminated (not “there is no noise”) M1 because pulses can be regenerated A1 e.g. much greater data handling/carrying capacity M1 because many messages can be carried at the same time/greater bandwidth A1 e.g. more secure (M1) because it can be encrypted (A1) e.g. error checking (M1) because extra information/parity bit can be added (A1) [4] (allow any two sensible suggestions with ‘state’ M1 and ‘explain’ A1) (b) attenuation = 10 lg (145 / 29) (= 7.0) C1 attenuation per unit length = 7.0 / 36 = 0.19 dB km–1 A1 [2]

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