Cambridge A Level Physics 9702 — 2002 Oct/Nov Paper 4 · Variant 1

TIME 1 hour INSTRUCTIONS TO CANDIDATES Write your name, Centre number and candidate number in the spaces at the top of this page. Answer all questions. Write your answers in the spaces provided on the question paper. INFORMATION FOR CANDIDATES 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. CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level PHYSICS 9702/4 PAPER 4 A2 Core OCTOBER/NOVEMBER SESSION 2002 1 hour Candidates answer on the question paper. No additional materials. This question paper consists of 15 printed pages and 1 blank page. SPA (NH/PW) S21697/3 © CIE 2002 [Turn over Candidate Centre Number Number Candidate Name FOR EXAMINER’S USE

2 9702/4 O/N/02 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

3 9702/4 O/N/02 [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

4 9702/4 O/N/02 Answer all the questions in the spaces provided. 1 A kettle is rated as 2.3 kW. A mass of 750 g of water at 20 °C is poured into the kettle. When the kettle is switched on, it takes 2.0 minutes for the water to start boiling. In a further 7.0 minutes, one half of the mass of water is boiled away. (a) Estimate, for this water, (i) the specific heat capacity, specific heat capacity = … J kg–1K–1 (ii) the specific latent heat of vaporisation. specific latent heat = … J kg–1 [5] (b) State one assumption made in your calculations, and explain whether this will lead to an overestimation or an underestimation of the value for the specific latent heat. … … …[2] For Examiner’s Use

5 9702/4 O/N/02 [Turn over 2 Fig. 2.1 gives information on three lines observed in the emission spectrum of hydrogen atoms. Fig. 2.1 (a) Complete Fig. 2.1 by calculating the photon energy for the wavelength of 486 nm. [2] (b) Fig. 2.2 is a partially completed diagram to show energy levels of a hydrogen atom. Fig. 2.2 On Fig. 2.2 draw one further labelled energy level, and complete the diagram with arrows to show the energy changes for the other two wavelengths. [3] wavelength of photon = 656mm 3.03 x 10-19 J level L energy above level L For Examiner’s Use wavelength/nm 656 486 1880 photon energy / 10–19J 3.03 … 1.06

6 9702/4 O/N/02 3 A student sets out to investigate the oscillation of a mass suspended from the free end of a spring, as illustrated in Fig. 3.1. Fig. 3.1 The mass is pulled downwards and then released. The variation with time t of the displacement y of the mass is shown in Fig. 3.2. Fig. 3.2 (a) Use information from Fig. 3.2 (i) to explain why the graph suggests that the oscillations are undamped, … 2 1 -1 -2 0 0 0.5 1.0 1.5 2.0 2.5 t/s y/cm spring mass oscillation of mass For Examiner’s Use

7 9702/4 O/N/02 [Turn over (ii) to calculate the angular frequency of the oscillations, angular frequency = … rad s–1 (iii) to determine the maximum speed of the oscillating mass. speed = … m s–1 [6] (b) (i) Determine the resonant frequency f0 of the mass-spring system. f0 = … Hz (ii) The student finds that if short impulsive forces of frequency
 f0 are impressed on the mass-spring system, a large amplitude of oscillation is obtained. Explain this observation. … … … [3] For Examiner’s Use

8 9702/4 O/N/02 4 If an object is projected vertically upwards from the surface of a planet at a fast enough speed, it can escape the planet’s gravitational field. This means that the object can arrive at infinity where it has zero kinetic energy. The speed that is just enough for this to happen is known as the escape speed. (a) (i) By equating the kinetic energy of the object at the planet’s surface to its total gain of potential energy in going to infinity, show that the escape speed v is given by v2 = , where R is the radius of the planet and M is its mass. (ii) Hence show that v2 = 2Rg, where g is the acceleration of free fall at the planet’s surface. [3] 2GM R For Examiner’s Use

9 9702/4 O/N/02 [Turn over (b) The mean kinetic energy Ek of an atom of an ideal gas is given by Ek = 3 2 kT, where k is the Boltzmann constant and T is the thermodynamic temperature. Using the equation in (a)(ii), estimate the temperature at the Earth’s surface such that helium atoms of mass 6.6 ×10–27kg could escape to infinity. You may assume that helium gas behaves as an ideal gas and that the radius of Earth is 6.4 ×106m. temperature = … K [4] 5 Some capacitors are marked ‘48 µF, safe working voltage 25 V’. Show how a number of these capacitors may be connected to provide a capacitor of capacitance (a) 48 µF, safe working voltage 50 V, [2] (b) 72 µF, safe working voltage 25 V. [2] For Examiner’s Use

10 9702/4 O/N/02 6 (a) A charged particle may experience a force in an electric field and in a magnetic field. State two differences between the forces experienced in the two types of field. 1. … … 2. … …[4] (b) A proton, travelling in a vacuum at a speed of 4.5 ×106m s–1, enters a region of uniform magnetic field of flux density 0.12 T. The path of the proton in the field is a circular arc, as illustrated in Fig. 6.1. Fig. 6.1 (i) State the direction of the magnetic field. … (ii) Calculate the radius of the path of the proton in the magnetic field. radius = … m [4] region of uniform magnetic field path of proton path of proton For Examiner’s Use

11 9702/4 O/N/02 [Turn over (c) A uniform electric field is now created in the same region as the magnetic field in Fig. 6.1, so that the proton passes undeviated through the region of the two fields. (i) On Fig. 6.1 mark, with an arrow labelled E, the direction of the electric field. (ii) Calculate the magnitude of the electric field strength. field strength = … V m–1 [3] (d) Suggest why gravitational forces on the proton have not been considered in the calculations in (b) and (c). … …[1] For Examiner’s Use

12 9702/4 O/N/02 7 A metal wire is held taut between the poles of a permanent magnet, as illustrated in Fig. 7.1. Fig. 7.1 A cathode-ray oscilloscope (c.r.o.) is connected between the ends of the wire. The Y-plate sensitivity is adjusted to 1.0 mV cm–1 and the time base is 0.5 ms cm–1. The wire is plucked at its centre. Fig. 7.2 shows the trace seen on the c.r.o. Fig. 7.2 1.0cm 1.0cm clamp wire For Examiner’s Use

13 9702/4 O/N/02 [Turn over (a) Making reference to the laws of electromagnetic induction, suggest why (i) an e.m.f. is induced in the wire, … … … (ii) the e.m.f. is alternating. … … … [4] (b) Use Fig. 7.2 and the c.r.o. settings to determine the equation representing the induced alternating e.m.f. equation: … [4] For Examiner’s Use

14 9702/4 O/N/02 8 (a) Define the term radioactive decay constant. … … …[2] (b) State the relation between the activity A of a sample of a radioactive isotope containing N atoms and the decay constant λ of the isotope. …[1] (c) Radon is a radioactive gas with half-life 56 s. For health reasons, the maximum permissible level of radon in air in a building is set at 1 radon atom for every 1.5 ×1021 molecules of air. 1 mol of air in the building is contained in 0.024 m3. Calculate, for this building, (i) the number of molecules of air in 1.0 m3, number = … (ii) the maximum permissible number of radon atoms in 1.0 m3 of air, number = … For Examiner’s Use

15 9702/4 O/N/02 (iii) the maximum permissible activity of radon per cubic metre of air. activity = … Bq [5] For Examiner’s Use

CAMBRIDGE INTERNATIONAL EXAMINATIONS NOVEMBER 2002 GCE Advanced Level UNIVERSITY of CAMBRIDGE Local Examinations Syndicate

Page 1 of 3 Mark Scheme Syllabus A Level Examinations — November 2002 9702 Paper 4 1@@ co) ) 2 (a) E = he/A = (6.63 x 10 x 3.0 x 10°) / (486 x 10°) (b) 3@ @ Gi) Gi ) @ (i) 4@@ i) (b) QD = MCAD oeecccccseeecece setts nsccesenecesseeneccanecceeueeseneesseenes cl 2300 = 0.75 xc x(100—20)/120 ...(ifuses +273, then —2)… Cl c = 46003 kg’ K" we ” Q=mL 2300 = (0.375 /420) x L L = 2.6x 10°F kg! ...(alow 1 Sf)…ccccccecceseecsceteeeeeseseeeee Al e.g. heat losses, power not constant etc …eeeeeeeeeeseeeeeeeeee M1 (do not allow if releated to s.h.c., rather than I.h.c.) effect on'value for Loo... ccc cee ceecc eee eccecceeceeeceeceeeceeeeeeeeeese Al = 4.09x 10°F ...(allow2 sf) energy level drawn at 4.09 x 107 J transition 4.09 x 107° to zero clear transition 4.09 x 10°” to 3.03 x 10° clear (-1 for reversed arrows, -1 for extra level at 1.06) constant amplitude period = 0.75s_ ...(allow 40.2 s). @=2nT … @= 84rads? ...(-1 for 1 sf).. either use of gradient or v = ayo v = 0.168ms" (allow +0.02 for construction: gradient drawn at wrong place 0/2) LBZ ceecccceccessseeseeecceeneeceeceeeeceesceceeeeeseneceseeeeeereeeeeraes at fo, ‘pulse’ provided to mass on alternate/some oscillations … so ‘pulses’ build up the amplitude ooo... eeeeeeeeeeeeee Al g=GM/R … clear algebra giving v= Ym = 3/2kT = 3kT/m 3KT/m =2gR ... . T = (2x 6.6 x 1027 x 9.81 x 6-4 x 10) /(1.38 x 102 x x3) eee Cl T = 20x 108K eeeeeeccesceceesceesesceneeseeecensensessessseesetssens Al [5] [2] [2] 3) [6] 3] (3) [4]

Page 2 of 3 Mark Scheme Syllabus [ Paper | A Level Examinations — November 2002 9702 4 | 5 (a) two capacitors in series z or any circuit such that V< 25 V across any C …ecceeeseeeeeeeee Bl in parallel with second series pair or any correct combination … Bl [2] (b) two capacitors in series in parallel with a single capacitor or other correct combination …:::ecceeeeeeesseeeeeeeeeenenenee B2 [2] (leads not shown, then —1 overall) 6. (a) e.g. E-field, force independent of speed, B-field, force « speed ... B2. E-field, force along field direction, B-field, force normalete ...B2 [4] (b) () out of plane of paper (not ‘upwards’).. (id rm D7 = BQV cecessccccsnecsseeeeeceeeee . = (1,67 «1097 «4.5 x 109)/ (0.12 « 16 x 10) .Cl r= 039m seteeeeeeeees Al [4] (c) () arrow pointing up page (ii) Bav = Eq E = 0.12 x 4.5 x 10° = SAO Vi ie eeceeecccesceceeseeseeeececceceeseseceseeseeesees Al [3] (d) gravitational force << Fg Or Fe …eccecceceeseeeeeeeeeeeeeeeeeeeeees Bl [i] 7 (a) (i) the wire cuts magnetic field 02. …e cece cette eeeeneeeeeeeeeeeee e.m.f. induced when there is a change/cutting of flux... (ii) (Lenz) e.m.f. ‘opposes’ change causingit … as direction of movement changes, so does e.m.f. [4] (b) xo = 1.5mV_...(allow +0.1) wa. Cl @ = 2n/T = 2n/(3 x 10°) Cl = 2090rads" … . Cl x = 1.5sin2090t … we we we aw Al [4]

Pages of3 Mark Scheme Syllabus | Paper _| ALevel Examinations —- November 2002 9702 4 | 8 (a) probability of decay of a nucleus per unit time [2} (b) A = AN ...AiQMOTE SIGN)... …ccecceeeeeeeteesteeseeeeeecesseeneeee Bl] () @ 1m’ contains 1/0.024 = 41.7 mol ceecceccececceces-. 1 m’ contains 41.7x Na = 2.5 x 10 molecules (i) number = (2.5 x 107) /(1.5 x 10?!) = 1.67 x 104 (iii) AT, = 0.693 A = 0.693 /56 = 0.01248 ec cccecescceecesesesseceeseeececese Cl activity = 0.0124 x 1.67 x 10¢ F210 BQ eeseseccescesseesesscecsssescssevstecestetscesveveneze Al [5]