Cambridge A Level Physics 9702 — 2024 May/June Paper 4 · Variant 1

1 (a) Define gravitational potential at a point. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [2] (b) A satellite X, of mass M, orbits a planet at a constant distance 4R from the centre of the planet, as shown in Fig. 1.1. planet orbit of Y satellite X, mass M R 4R satellite Y, mass 2M orbit of X Fig. 1.1 (not to scale) A second satellite Y, of mass 2M, orbits the planet with orbital radius R. The gravitational potential at X due to the planet is –Φ. The planet is a uniform sphere. (i) Explain why the gravitational potential at X is negative. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [2] (ii) State an expression, in terms of Φ, for the gravitational potential at Y due to the planet. gravitational potential = ......................................................... [2] (iii) Complete Table 1.1 by giving expressions, in terms of some or all of M, R and Φ, for the quantities indicated for each of the satellites X and Y. Table 1.1 satellite X satellite Y gravitational field strength at satellite due to planet gravitational potential energy of satellite [4] [Total: 10]

Mark scheme: 1(a) work done per unit mass B1 work done moving mass from infinity (to the point) B1 1(b)(i) potential is zero at infinity B1 work is done by (two) masses in moving them closer together or work is done on (two) masses in moving them apart B1 1(b)(ii) magnitude of potential shown as 4 B1 potential negative and shown as a multiple of – [potential = –4 if fully correct] B1 1(b)(iii) field strength at X:  / 4R A1 field strength at Y: 4 / R A1 potential energy at X: –M A1 potential energy at Y: –8M A1

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2 (a) (i) State the magnitude and unit of absolute zero on the thermodynamic temperature scale. ..................................................................................................................................... [1] (ii) Explain why temperature measured using a laboratory liquid-in-glass thermometer does not give a measurement of thermodynamic temperature. ........................................................................................................................................... ..................................................................................................................................... [1] (b) Fig. 2.1 shows a simplified diagram of a type of thermometer called a platinum resistance thermometer. plastic strip platinum wire X Y large glass tube Fig. 2.1 The glass tube is immersed in the environment for which the temperature is to be determined. The resistance between the terminals X and Y is measured. Fig. 2.2 shows the variation of the resistivity ρ of platinum with thermodynamic temperature T. ρ 0 T Fig. 2.2 (i) Explain how Fig. 2.2 shows that platinum is a suitable metal for use in a resistance thermometer. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [2] (ii) Suggest a reason why a platinum resistance thermometer is not suitable for measuring a rapidly changing temperature. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [1] (iii) Suggest a type of thermometer that is suitable for measuring a rapidly changing temperature. ..................................................................................................................................... [1] (c) A negative temperature coefficient thermistor may be used as a type of resistance thermometer. State one way in which the variation with temperature of the resistance of a thermistor differs from that of a platinum wire. ................................................................................................................................................... ............................................................................................................................................. [1] [Total: 7]

Mark scheme: 2(a)(i) 0 K B1 2(a)(ii) (measurement) depends on properties of the liquid B1 2(b)(i)  resistivity varies with temperature  variation with temperature is linear  unique value of resistivity for each (different value of) temperature Any two points, 1 mark each B2 2(b)(ii) thermometer has high heat capacity/specific heat capacity or energy transfer needed for thermometer to reach correct temperature or thermometer takes time to reach the correct temperature B1 2(b)(iii) thermocouple B1 2(c) (variation is) inverse or (variation is) non-linear B1

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3 (a) (i) State what is meant by an ideal gas. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [2] (ii) Use one of the basic assumptions of the kinetic theory to explain what can be deduced about the potential energy associated with the random motion of molecules in an ideal gas. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [2] (b) A sample of 0.26 m3 of an ideal gas is at pressure 2.0 × 105 Pa and temperature 290 K. Determine: (i) the number N of molecules of the gas N = ......................................................... [2] (ii) the average translational kinetic energy EK of one molecule of the gas EK = ...................................................... J [2] (iii) the internal energy of the gas. Explain your reasoning. internal energy = ...................................................... J [2] (c) The volume V of the gas in (b) is now varied, keeping its pressure constant. On Fig. 3.1, sketch the variation with V of the internal energy U of the gas. U 0 0 V Fig. 3.1 [2] [Total: 12]

Mark scheme: 3(a)(i) M1 where T is thermodynamic temperature A1 3(a)(ii) no intermolecular forces B1 (so) potential energy is zero B1 3(b)(i) pV = NkT C1 N = (2.0  105  0.26) / (1.38  10–23  290) = 1.3  1025 A1 3(b)(ii) EK = (3/2) kT C1 EK = (3/2)  1.38  10–23  290 = 6.0  10–21 J A1 3(b)(iii) internal energy = total KE + PE of molecules or PE = 0 so internal energy = total KE of molecules B1 internal energy = 1.3  1025  6.0  10–21 = 7.8  104 J A1 3(c) straight line with positive gradient B1 line passing through the origin B1

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4 (a) State what is meant by resonance. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [2] (b) A small ball is held in place using a stretched string. One end of the string is fixed to a wall and the other end is attached to a vibration generator, as shown in Fig. 4.1. ball wall vibration generator string Fig. 4.1 Initially, the vibration generator is switched off. A student displaces the ball vertically and then releases it. Fig. 4.2 shows the variation of the displacement of the ball with time after it is released. displacement 0 0 0.1 0.2 0.3 0.4 0.5 0.6 time / s Fig. 4.2 (i) State the name of the phenomenon illustrated by the decrease in the amplitude of the oscillations in Fig. 4.2. ..................................................................................................................................... [1] (ii) Explain the decrease with time of the amplitude of the oscillations of the ball. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [2] (iii) Determine the frequency of the oscillations of the ball. frequency = .................................................... Hz [1] (c) The vibration generator in (b) is switched on and its frequency f of vibration is gradually increased from 0 to 10 Hz. On Fig. 4.3, sketch the variation with f of the amplitude of the oscillations of the ball. amplitude 0 0 2.5 5.0 7.5 10.0 f / Hz Fig. 4.3 [2] [Total: 8]

Mark scheme: 4(a) oscillation (of object) at maximum amplitude B1 when driving frequency = natural frequency (of system) B1 4(b)(i) light damping B1 4(b)(ii) oscillations (of ball) lose energy B1 (due to) resistive forces (acting on ball) B1 4(b)(iii) frequency = 1 / 0.25 = 4.0 Hz A1 4(c) curve showing a maximum amplitude at a single non-zero frequency B1 single maximum amplitude shown at 4.0 Hz B1

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5 (a) Define electric field. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [2] (b) Fig. 5.1 shows two parallel conducting plates that are in a vacuum. The plates are separated by a distance of 6.7 cm and have a potential difference (p.d.) of 430 V between them. +430 V conducting plate electron, speed 6.7 cm 2.6 × 107 m s–1 conducting plate 0 V Fig. 5.1 (i) On Fig. 5.1, draw four field lines to represent the electric field between the plates. [2] (ii) Determine the strength E of the electric field between the plates. E = ............................................... N C–1 [2] (iii) An electron travels at a speed of 2.6 × 107 m s–1 towards the region between the plates, as shown in Fig. 5.1. On Fig. 5.1, draw the path of the electron as it moves between and beyond the plates. [2] (c) A uniform magnetic field is now applied in the region of the electric field in Fig. 5.1, so that the electron in (b)(iii) travels undeviated through the region. (i) Determine the direction of the uniform magnetic field. ..................................................................................................................................... [1] (ii) Explain, with reference to the forces exerted by the two fields on the electron, why the path of the electron is undeviated. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [2] (iii) Determine the flux density B of the uniform magnetic field. Give a unit with your answer. B = ................................. unit ............... [2] [Total: 13]

Mark scheme: 5(a) force per unit charge B1 force on positive charge B1 5(b)(i) four straight vertical parallel lines, approximately evenly spaced B1 arrows downwards B1 5(b)(ii) E = V / d C1 E = 430 / 0.067 = 6.4  103 N C–1 A1 5(b)(iii) smooth curve within plates and straight lines outside plates B1 direction of deflection shown as upwards B1 5(c)(i) into the page B1 5(c)(ii) forces are in opposite directions B1 (undeviated) when (magnitudes of) forces are equal B1 5(c)(iii) Eq = Bqv C1 B = E / v = (6.4  103) / (2.6  107) = 2.5  10–4 T A1

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6 Fig. 6.1 shows a capacitor of capacitance C connected in series with a resistor of resistance R. C R Fig. 6.1 Initially the switch is open and there is a p.d. of 12 V across the capacitor. At time t = 0, the switch is closed so that there is a current I in the resistor. Fig. 6.2 shows the variation of I with t. 0.2 I / mA 0.1 0 0 2 4 6 8 t / s Fig. 6.2 (a) Explain the shape of the line in Fig. 6.2. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [3] (b) Use Fig. 6.2 to determine: (i) resistance R R = ..................................................... Ω [2] (ii) the time constant τ of the circuit in Fig. 6.1. τ = ...................................................... s [3] (c) Use your answers in (b) to determine capacitance C. C = ...................................................... F [2] [Total: 10]

Mark scheme: 6(a) p.d. across capacitor proportional to charge on capacitor  p.d. across capacitor = p.d. across resistor  current in resistor proportional to p.d. across resistor  current in resistor = rate of decrease of charge on capacitor Any two points, 1 mark each B2 charge proportional to current so rate of decrease of current decreases as current decreases (therefore exponential shape) B1 6(b)(i) R = V / I = 12 / (0.13  10–3) C1 = 9.2  104  A1 6(b)(ii) correct read-off of at least one pair of values for I and t C1 attempted read-off of t when I = 0.048 mA or substitution of a correct pair of values of I and t into I = 0.13 exp (– t / ) C1  = 4.3 s A1 6(c)  = RC C1 C =  / R = 4.3 / (9.2  104) = 4.7  10–5 F A1

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7 A circuit contains a power supply that provides a sinusoidal alternating input voltage VIN. There is an output voltage VOUT across a load resistor R, as shown in Fig. 7.1. VIN R VOUT Fig. 7.1 (a) State the purpose of the circuit in Fig. 7.1. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [2] (b) Fig. 7.2 shows the variation of VOUT with time t. 10 VOUT / V 5 0 0 0.02 0.04 0.06 0.08 t / s Fig. 7.2 (i) The load resistor R has a resistance of 370 Ω. Show that the maximum power dissipated in R is 0.22 W. [2] (ii) On Fig. 7.3, sketch the variation with t of the power P dissipated in R. 0.4 P / W 0.2 0 0 0.02 0.04 0.06 0.08 t / s Fig. 7.3 [3] (iii) Calculate the mean power dissipated in R. mean power = ..................................................... W [1] (c) The circuit of Fig. 7.1 is disconnected, and R is connected directly across the power supply. Explain, without calculation, how the mean power now dissipated in R compares with the answer in (b)(iii). ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [2] [Total: 10]

Mark scheme: 7(a) rectification (of the input voltage) M1 full-wave A1 7(b)(i) P = V2 / R or maximum V = 9.0 V C1 PMAX = 9.02 / 370 = 0.22 W A1 7(b)(ii) sinusoidal shape with minima sitting on the time axis B1 correct frequency and phase, with minima at 0, 0.02, 0.04, 0.06 and 0.08 s and maxima at 0.01, 0.03, 0.05 and 0.07 s B1 all maxima shown at 0.22 W B1 7(b)(iii) mean power = peak power / 2 = 0.22 / 2 = 0.11 W A1 7(c) power–time graph is identical B1 (so) mean powers are equal B1

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8 (a) State what is meant by a photon. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [2] (b) Fig. 8.1 shows a tube in which X-rays are produced at a metal target. X Y particles filament vacuum glass tube metal target Fig. 8.1 Particles are accelerated from the filament to the target by a constant high voltage applied across the terminals X and Y. (i) State the name of the particles. ..................................................................................................................................... [1] (ii) On Fig. 8.1, use + and – signs to label terminals X and Y to indicate the polarity of the high voltage. [1] (c) For an accelerating voltage of 32 kV in Fig. 8.1, determine: (i) the maximum energy, in MeV, of an X-ray photon produced at the target maximum photon energy = ................................................. MeV [1] (ii) the maximum momentum of an X-ray photon produced at the target maximum photon momentum = ................................................... N s [2] (iii) the minimum wavelength of X-rays produced at the target. minimum wavelength = ..................................................... m [3] (d) Explain why X-rays can be used to produce images of internal body structures that have good contrast. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [3] [Total: 13]

Mark scheme: 8(a) packet / quantum of energy M1 of electromagnetic radiation A1 8(b)(i) electron(s) B1 8(b)(ii) X labelled – and Y labelled + B1 8(c)(i) 0.032 MeV A1 8(c)(ii) momentum = E / c C1 momentum = (0.032 × 1.60  10–13) / (3.00  108) = 1.7  10–23 N s A1 8(c)(iii) E = hf and  = c / f C1  = hc / E = (6.63  10–34 × 3.00  108) / (0.032  1.60 × 10–13) C1  = 3.9  10–11 m A1 8(d) discussion of bone and soft tissue B1 discussion of different attenuation (coefficients) or discussion differences in penetration / transmission / absorption B1 transmitted intensities (by bone and tissue) are very different (leading to good contrast images) B1

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9 (a) Define half-life of a radioactive isotope. ................................................................................................................................................... ................................................................................................................................................... ............................................................................................................................................. [1] (b) Radioactive isotope X decays to isotope Y. A sample contains only nuclei of X at time t = 0. Fig. 9.1 shows the variation with t of the numbers of nuclei of X and of Y as the sample decays. 4 Y number of nuclei / 1022 3 2 1 X 0 0 10 20 30 40 50 60 t / s Fig. 9.1 (i) State the name of the quantity represented by the magnitude of the gradient of line X in Fig. 9.1. ..................................................................................................................................... [1] (ii) State three conclusions about X or Y that may be drawn from Fig. 9.1. The conclusions may be qualitative or quantitative. Use the space below for any working that you need. 1 ........................................................................................................................................ ........................................................................................................................................... 2 ........................................................................................................................................ ........................................................................................................................................... 3 ........................................................................................................................................ ........................................................................................................................................... [3] (c) The mass of radioactive isotope X in the sample in (b) is 7.3 × 10–4 kg at time t = 0. Determine the nucleon number of isotope X. nucleon number = ......................................................... [3] [Total: 8]

Mark scheme: 9(a) time for activity (of sample) to halve B1 9(b)(i) activity (of X at time t) B1 9(b)(ii)  Y is a stable isotope  total number of nuclei is constant  half-life (of X) is 13.6 s  decay constant (of X) is 0.051 s–1  amount (of X) at t = 0 is 0.066 mol  activity (of X) at t = 0 is 2.0  1021 Bq Any three points, 1 mark each B3 9(c) mass of 1 nucleus = (7.3  10–4) / (4.0  1022) C1 nucleon number = mass of nucleus / (1.66  10–27) C1 = (7.3  10–4) / (4.0 × 1022  1.66 × 10–27) = 11 and given as an integer A1

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10 (a) (i) State what is meant by the luminosity of a star. ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [2] (ii) Explain how a standard candle in a distant galaxy can be used to determine the distance of the galaxy from an observer. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... ..................................................................................................................................... [3] (b) The Sun has a radius of 6.96 × 108 m and a surface temperature of 5780 K. Light from the Sun is observed to have a peak intensity at a wavelength of 501 nm. (i) Calculate the luminosity of the Sun. Give a unit with your answer. luminosity = ................................. unit ............... [2] (ii) Another star emits radiation that has a peak intensity at a wavelength of 624 nm. Determine the surface temperature of this star. surface temperature = .......................................................K [2] [Total: 9]

Mark scheme: 10(a)(i) total power B1 power radiated (by the star) B1 10(a)(ii) standard candle has known luminosity B1 radiant flux intensity measured by observer B1 (distance calculated using) F = L / 4d2 B1 10(b)(i) luminosity = 4 r2T4 = 4  5.67  10–8  (6.96  108)2 × 57804 C1 = 3.85 × 1026 W A1 10(b)(ii) MAXT = constant C1 temperature = (5780  501) / 624 = 4640 K A1

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