Cambridge A Level Physics 9702 — 2004 May/June Paper 4 · Variant 1

This document consists of 15 printed pages and 1 blank page. SP (NF/JG) S53572/2 © UCLES 2004 [Turn over UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level PHYSICS 9702/04 Paper 4 May/June 2004 1 hour Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen in the spaces provided on the Question Paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. You may lose marks if you do not show your working or if you do not use appropriate units. Centre Number Candidate Number Name For Examiner’s Use 1 2 3 4 5 6 7 8 Total If you have been given a label, look at the details. If any details are incorrect or missing, please fill in your correct details in the space given at the top of this page. Stick your personal label here, if provided.

2 9702/04/M/J/04 Data speed of light in free space, c = 3.00 × 108 m s–1 permeability of free space,
0 = 4 × 10–7 H m–1 permittivity of free space, 0 = 8.85 × 10–12 F m–1 elementary charge, e = 1.60 × 10–19 C the Planck constant, h = 6.63 × 10–34 J s unified atomic mass constant, u = 1.66 × 10–27 kg rest mass of electron, me = 9.11 × 10–31 kg rest mass of proton, mp = 1.67 × 10–27 kg molar gas constant, R = 8.31 J K–1 mol–1 the Avogadro constant, NA = 6.02 × 1023 mol–1 the Boltzmann constant, k = 1.38 × 10–23 J K–1 gravitational constant, G = 6.67 × 10–11 N m2 kg–2 acceleration of free fall, g = 9.81 m s–2 © UCLES 2004

3 9702/04/M/J/04 [Turn over Formulae uniformly accelerated motion, s = ut +
 at 2 v2 = u2 + 2as work done on/by a gas, W = pV gravitational potential, φ = – simple harmonic motion, a = –
2x velocity of particle in s.h.m., v = v0 cos
t v = ±
√(x2 0 – x2) resistors in series, R = R1 + R2 + . . . resistors in parallel, 1/R = 1/R1 + 1/R2 + . . . electric potential, V = capacitors in series, 1/C = 1/C1 + 1/C2 + . . . capacitors in parallel, C = C1 + C2 + . . . energy of charged capacitor, W =
 QV alternating current/voltage, x = x0 sin
t hydrostatic pressure, p = qgh pressure of an ideal gas, p =
 <c2> radioactive decay, x = x0 exp(– t) decay constant,  = critical density of matter in the Universe, q0 = equation of continuity, Av = constant Bernoulli equation (simplified), p1 +
 qv2 1 = p2 +
 qv2 2 Stokes’ law, F = Arv Reynolds’ number, Re = drag force in turbulent flow, F = Br2qv2 qvr  3H0 2 8G 0.693 t
 Nm V Q 40r Gm r © UCLES 2004

4 9702/04/M/J/04 Answer all the questions in the spaces provided. 1 (a) State the significance of the Millikan experiment. … … [1] (b) In the Millikan experiment, oil droplets were found to have the following charges. 1.56 × 10–19 C 4.88 × 10–19 C 1.64 × 10–19 C 3.14 × 10–19 C 4.76 × 10–19 C Use these data to determine a value for the elementary charge. Explain your working. … … elementary charge = … C [2] For Examiner’s Use © UCLES 2004

5 9702/04/M/J/04 [Turn over 2 The pressure p of an ideal gas is given by the expression p = <c2> . (a) Explain the meaning of the symbol <c2>. … … [2] (b) The ideal gas has a density of 2.4 kg m–3 at a pressure of 2.0 × 105 Pa and a temperature of 300 K. (i) Determine the root-mean-square (r.m.s.) speed of the gas atoms at 300 K. r.m.s. speed = … m s–1 [3] (ii) Calculate the temperature of the gas for the atoms to have an r.m.s. speed that is twice that calculated in (i). temperature = … K [3] Nm V 1 3 For Examiner’s Use © UCLES 2004

6 9702/04/M/J/04 3 A binary star consists of two stars that orbit about a fixed point C, as shown in Fig. 3.1. Fig. 3.1 The star of mass M1 has a circular orbit of radius R1 and the star of mass M2 has a circular orbit of radius R2. Both stars have the same angular speed ω, about C. (a) State the formula, in terms of G, M1, M2, R1, R2 and ω for (i) the gravitational force between the two stars, … (ii) the centripetal force on the star of mass M1. … [2] (b) The stars orbit each other in a time of 1.26 × 108 s (4.0 years). Calculate the angular speed ω for each star. angular speed = … rad s–1 [2] M1 R1 R2 M2 C For Examiner’s Use © UCLES 2004

7 9702/04/M/J/04 [Turn over (c) (i) Show that the ratio of the masses of the stars is given by the expression = . [2] (ii) The ratio is equal to 3.0 and the separation of the stars is 3.2 × 1011 m. Calculate the radii R1 and R2. R1 = … m R2 = … m [2] (d) (i) By equating the expressions you have given in (a) and using the data calculated in (b) and (c), determine the mass of one of the stars. mass of star = … kg (ii) State whether the answer in (i) is for the more massive or for the less massive star. … [4] M1 M2 R2 R1 M1 M2 For Examiner’s Use © UCLES 2004

8 9702/04/M/J/04 4 A vertical spring supports a mass, as shown in Fig. 4.1. Fig. 4.1 The mass is displaced vertically then released. The variation with time t of the displacement y from its mean position is shown in Fig. 4.2. Fig. 4.2 For Examiner’s Use © UCLES 2004 y / cm +2 0 –1 –2 +1 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 t / s

9 9702/04/M/J/04 [Turn over A student claims that the motion of the mass may be represented by the equation y = y0sinωt. (a) Give two reasons why the use of this equation is inappropriate. 1. … … 2. … … [2] (b) Determine the angular frequency ω of the oscillations. angular frequency = … rad s–1 [2] (c) The mass is a lump of plasticine. The plasticine is now flattened so that its surface area is increased. The mass of the lump remains constant and the large surface area is horizontal. The plasticine is displaced downwards by 1.5 cm and then released. On Fig. 4.2, sketch a graph to show the subsequent oscillations of the plasticine. [3] For Examiner’s Use © UCLES 2004

10 9702/04/M/J/04 5 (a) Explain, in terms of heating effect, what is meant by the root-mean-square (r.m.s.) value of an alternating current. … … … [2] (b) State the relation between the peak current I0 and the r.m.s. current Irms of a sinusoidally-varying current. … [1] (c) The value of a direct current and the peak value of a sinusoidal alternating current are equal. (i) Determine the ratio power dissipation in a resistor of resistance R by the direct current ————————————————————————————————— . power dissipation in the resistor of resistance R by the alternating current ratio = … [2] (ii) State one advantage and one disadvantage of the use of alternating rather than direct current in the home. advantage … … disadvantage … … [2] For Examiner’s Use © UCLES 2004

11 9702/04/M/J/04 [Turn over (d) A current I varies with time t as shown in Fig. 5.1. Fig. 5.1 For this varying current, state (i) the peak value, peak value = … A [1] (ii) the r.m.s. value. r.m.s. value = … A [1] I / A +4 0 –2 –3 –1 –4 +2 +1 +3 0 1 2 3 4 5 t / ms For Examiner’s Use © UCLES 2004

12 9702/04/M/J/04 6 The first law of thermodynamics may be expressed in the form ∆U = q + w, where U is the internal energy of the system, ∆U is the increase in internal energy, q is the thermal energy supplied to the system, w is the work done on the system. Complete Fig. 6.1 for each of the processes shown. Write down the symbol ‘+’ for an increase, the symbol ‘–’ to indicate a decrease and the symbol ‘0’ for no change, as appropriate. [6] Fig. 6.1 For Examiner’s Use © UCLES 2004 U q w the compression of an ideal gas at constant temperature the heating of a solid with no expansion the melting of ice at 0 °C to give water at 0 °C (Note: ice is less dense than water)

13 9702/04/M/J/04 [Turn over 7 (a) State the de Broglie relation, explaining any symbols you use. … … … [2] (b) An electron of mass m has kinetic energy E. Show that the de Broglie wavelength λ of this electron is given by [2] (c) Calculate the potential difference through which an electron, initially at rest, must be accelerated so that its de Broglie wavelength is equal to 0.40 nm (the diameter of an atom). potential difference = … V [3] λ = h mE 2 . For Examiner’s Use © UCLES 2004

14 9702/04/M/J/04 8 Fig. 8.1 shows the variation with nucleon number of the binding energy per nucleon of a nucleus. Fig. 8.1 (a) On Fig. 8.1, mark with the letter S the position of the nucleus with the greatest stability. [1] (b) One possible fission reaction is 235 92U + 1 0n → 144 56Ba + 90 36Kr + 21 0n. (i) On Fig. 8.1, mark possible positions for 1. the Uranium-235 (235 92U) nucleus (label this position U), 2. the Krypton-90 (90 36Kr) nucleus (label this position Kr). [1] (ii) The binding energy per nucleon of each nucleus is as follows. 235 92U: 1.2191 × 10–12 J 144 56Ba: 1.3341 × 10–12 J 90 36Kr: 1.3864 × 10–12 J binding energy per nucleon 0 0 nucleon number For Examiner’s Use © UCLES 2004

15 9702/04/M/J/04 Use these data to calculate 1. the energy release in this fission reaction (give your answer to three significant figures), energy = … J [3] 2. the mass equivalent of this energy. mass = … kg [2] (iii) Suggest why the neutrons were not included in your calculation in (ii). … … [1] For Examiner’s Use © UCLES 2004

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