Cambridge A Level Physics 9702 — 2016 May/June Paper 4 · Variant 2

1 A binary star consists of two stars A and B that orbit one another, as illustrated in Fig. 1.1. 2.8 × 108 km t VWDU $ VWDU % PDVV 0$ 3 PDVV 0% t G Fig. 1.1 The stars are in circular orbits with the centres of both orbits at point P, a distance d from the centre of star A. (a) (i) Explain why the centripetal force acting on both stars has the same magnitude. ........................................................................................................................................... ........................................................................................................................................... ...................................................................................................................................... [2] (ii) The period of the orbit of the stars about point P is 4.0 years. Calculate the angular speed ω of the stars. ω = ............................................. rad s−1 [2] (b) The separation of the centres of the stars is 2.8 × 108 km. The mass of star A is MA. The mass of star B is MB. MA The ratio is 3.0. MB (i) Determine the distance d. d = ................................................... km [3] (ii) Use your answers in (a)(ii) and (b)(i) to determine the mass MB of star B. Explain your working. MB = .................................................... kg [3] [Total: 10]

Mark scheme: 1 (a) (i) gravitational force provides/is the centripetal force B1 same gravitational force (by Newton III) B1 [2] (ii) ω = 2π / T = 2π / (4.0 × 365 × 24 × 3600) C1 = 5.0 (4.98) × 10–8 rad s–1 A1 [2] (b) (i) (centripetal force =) MAdω2 = MB(2.8 × 108 –d)ω2 or MAdA = MBdB C1 MA / MB = 3.0 = (2.8 × 108 – d) / d C1 d = 7.0 × 107 km A1 [3] (ii) GMAMB / (2.8 × 1011)2 = MAdω2 B1 MB = (2.8 × 1011)2 × dω2 / G = (2.8 × 1011)2 × (7.0 × 1010) × (4.98 × 10–8)2 / (6.67 × 10–11) C1 = 2.0 × 1029 kg A1 [3]

More questions on Kinematics of uniform circular motion

2 (a) State what is meant by (i) the Avogadro constant NA, ........................................................................................................................................... ...................................................................................................................................... [1] (ii) the mole. ........................................................................................................................................... ...................................................................................................................................... [2] (b) A container has a volume of 1.8 × 104 cm3. The ideal gas in the container has a pressure of 2.0 × 107 Pa at a temperature of 17 °C. Show that the amount of gas in the cylinder is 150 mol. [1] (c) Gas molecules leak from the container in (b) at a constant rate of 1.5 × 1019 s−1. The temperature remains at 17 °C. In a time t, the amount of gas in the container is found to be reduced by 5.0%. Calculate (i) the pressure of the gas after the time t, pressure = ................................................... Pa [2] (ii) the time t. t = ....................................................... s [3] [Total: 9]

Mark scheme: 2 (a) (i) number of atoms/nuclei in 12 g of carbon-12 B1 [1] (ii) amount of substance M1 containing NA (or 6.02 × 1023) particles/molecules/atoms or which contains the same number of particles/atoms/molecules as there are atoms in 12 g of carbon-12 A1 [2] (b) pV = nRT 2.0 × 107 × 1.8 × 104 × 10–6 = n × 8.31 × 290, so n = 149 mol or 150 mol A1 [1] (c) (i) V and T constant and so pressure reduced by 5.0% pressure = 0.95 × 2.0 × 107 C1 or calculation of new n (= 142.5 mol) and correct substitution into pV = nRT (C1) pressure = 1.9 × 107 Pa A1 [2] (ii) loss is 5 / 100 × 150 mol = 7.5 mol or ∆N = 4.52 × 1024 C1 t = (7.5 × 6.02 × 1023) / 1.5 × 1019 or t = 4.52 × 1024 / 1.5 × 1019 C1 = 3.0 × 105 s A1 [3]

More questions on Equation of state

3 (a) Explain what is meant by the statement that two bodies are in thermal equilibrium. ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [1] (b) Suggest suitable types of thermometer, one in each case, to measure (i) the temperature of the flame of a Bunsen burner, ...................................................................................................................................... [1] (ii) the change in temperature of a small crystal when it is exposed to a pulse of ultrasound energy. ...................................................................................................................................... [1] (c) Some water is heated so that its temperature changes from 26.5 °C to a final temperature of 38.0 °C. State, to an appropriate number of decimal places, (i) the change in temperature in kelvin, change = ..................................................... K [1] (ii) the final temperature in kelvin. final temperature = ..................................................... K [1] [Total: 5]

Mark scheme: 3 (a) no net energy transfer between the bodies or bodies are at the same temperature B1 [1] (b) (i) thermocouple, platinum/metal resistance thermometer, pyrometer B1 [1] (ii) thermistor, thermocouple B1 [1] (c) (i) change = 11.5 K B1 [1] (ii) final temperature = 311.2 K B1 [1]

More questions on Temperature scales

4 A metal block hangs vertically from one end of a spring. The other end of the spring is tied to a thread that passes over a pulley and is attached to a vibrator, as shown in Fig. 4.1. pulley vibrator spring block Fig. 4.1 (a) The vibrator is switched off. The metal block of mass 120 g is displaced vertically and then released. The variation with time t of the displacement y of the block from its equilibrium position is shown in Fig. 4.2. 3 y / cm 2 1 0 0 0.2 0.4 0.6 0.8 1.0 W / s –1 –2 –3 Fig. 4.2 For the vibrations of the block, calculate (i) the angular frequency ω, ω = ............................................. rad s−1 [2] (ii) the energy of the vibrations. energy = ...................................................... J [2] (b) The vibrator is now switched on. The frequency of vibration is varied from 0.7f to 1.3f where f is the frequency of vibration of the block in (a). For the block, complete Fig. 4.3 to show the variation with frequency of the amplitude of vibration. Label this line A. [3] amplitude 0 0.7I I 1.3I frequency Fig. 4.3 (c) Some light feathers are now attached to the block in (b) to increase air resistance. The frequency of vibration is once again varied from 0.7f to 1.3f. The new amplitude of vibration is measured for each frequency. On Fig. 4.3, draw a line to show the variation with frequency of the amplitude of vibration. Label this line B. [2] [Total: 9]

Mark scheme: 4 (a) (i) T = 0.60 s and ω = 2π / T C1 ω = 10 (10.47) rad s–1 A1 [2] (ii) energy = ½mω2x02 or ½mv2 and v = ωx0 C1 = ½ × 120 × 10–3 × (10.5)2 × (2.0 × 10–2)2 = 2.6 × 10–3 J A1 [2] (b) sketch: smooth curve in correct directions B1 peak at f M1 amplitude never zero and line extends from 0.7f to 1.3f A1 [3] (c) sketch: peaked line always below a peaked line A M1 peak not as sharp and at (or slightly less than) frequency of peak in line A A1 [2]

More questions on Simple harmonic oscillations

5 The signal from a radio station is amplitude modulated. (a) State what is meant by amplitude modulation (AM). ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [2] (b) The variation with frequency of the intensity of the signal from the radio station is shown in Fig. 5.1. intensity 0 193 198 203 frequency / kHz Fig. 5.1 State, for this signal, (i) the bandwidth, bandwidth = ................................................. kHz [1] (ii) the maximum audio frequency that is broadcast. maximum frequency = ................................................. kHz [1] (c) A transmission line of length 45 km has an attenuation per unit length of 2.0 dB km −1. The input power to the transmission line is 500 mW. The minimum acceptable signal-to-noise ratio is 24 dB for background noise of 5.0 × 10−13 W. (i) Calculate the minimum acceptable power output from the transmission line. power = .................................................... W [2] (ii) Use your answer in (i) to determine whether it is possible to transmit the signal along the transmission line. [2] [Total: 8]

Mark scheme: 5 (a) amplitude of the carrier wave varies M1 in synchrony with displacement of the information/audio signal A1 [2] (b) (i) 10 kHz A1 [1] (ii) 5 kHz A1 [1] (c) (i) 24 = 10 lg (PMIN / {5.0 × 10–13}) C1 PMIN = 1.3 (1.26) × 10–10 W A1 [2] (ii) 45 × 2 = 10 lg ({500 × 10–3} / P) P = 5.0 × 10–10 (W) M1 P > PMIN so yes A1 or maximum attenuation calculated to be 96 (dB) (M1) 96 dB > 2 × 45 dB so yes (A1) or maximum length of wire calculated to be 48 (km) (M1) actual length 45 km < 48 km so yes (A1) or maximum attenuation per unit length calculated to be 2.2 dB km–1 (M1) 2.2 dB km–1 > 2.0 dB km–1 so yes (A1) [2]

More questions on Characteristics of alternating currents

6 (a) By reference to electric field lines, explain why, for points outside an isolated spherical conductor, the charge on the sphere may be considered to act as a point charge at its centre. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [2] (b) Two isolated protons are separated in a vacuum by a distance x. (i) Calculate the ratio electric force between the two protons . gravitational force between the two protons ratio = ......................................................... [3] (ii) By reference to your answer in (i), suggest why gravitational forces are not considered when calculating the force between charged particles. ........................................................................................................................................... ...................................................................................................................................... [1] [Total: 6]

Mark scheme: 6 (a) lines perpendicular to surface or lines are radial M1 lines appear to come from centre A1 [2] (b) (i) FE = (1.6 × 10–19)2 / 4πε0x2 C1 FG = G × (1.67 × 10–27)2 / x2 C1 FE / FG = (1.6 × 10–19)2 × (8.99 × 109) / [(1.67×10–27)2 × (6.67×10–11)] = 1.2 (1.24) × 1036 A1 [3] (ii) FE ≫ FG B1 [1]

More questions on Electric force between point charges

7 (a) State two uses of capacitors in electrical circuits, other than for the smoothing of direct current. 1. .............................................................................................................................................. 2. .............................................................................................................................................. [2] (b) The combined capacitance between terminals A and B of the arrangement shown in Fig. 7.1 is 4.0 μF. & & A B Fig. 7.1 Two capacitors each have capacitance C and the remaining capacitors each have capacitance 3.0 μF. The potential difference (p.d.) between terminals A and B is 12 V. (i) Determine the capacitance C. C = ................................................... μF [2] (ii) Calculate the magnitude of the total positive charge transferred to the arrangement. charge = ................................................... μC [2] (iii) Use your answer in (ii) to state the magnitude of the charge on one plate of 1. a capacitor of capacitance C, charge = ......................................................... μC 2. a capacitor of capacitance 3.0 μF. charge = ......................................................... μC [2] [Total: 8]

Mark scheme: 7 (a) e.g. storing energy blocking d.c. in oscillator circuits in tuning circuits in timing circuits any two B2 [2] (b) (i) 1 / 6 + 1 / C + 1 / C = 1 / 4 C1 C = 24 µF A1 [2] (ii) Q = CV = 4.0 × 10–6 × 12 C1 = 48 µC A1 [2] (iii) 1. 48 µC A1 2. 24 µC A1 [2]

More questions on Capacitors and capacitance

8 An ideal operational amplifier (op-amp) has infinite voltage gain and infinite slew rate. (a) State what is meant by (i) the voltage gain, ........................................................................................................................................... ...................................................................................................................................... [1] (ii) infinite slew rate. ........................................................................................................................................... ........................................................................................................................................... ...................................................................................................................................... [2] (b) A non-inverting amplifier circuit incorporating an ideal op-amp is shown in Fig. 8.1. 5 – + ² 9 9,1 9287 Fig. 8.1 The supply to the op-amp is +9 V / −9 V. The voltage gain of the amplifier circuit is 12. Determine the resistance of resistor R. resistance = ..................................................... Ω [2] (c) For the circuit of Fig. 8.1, the variation with time t of the input potential VIN to the amplifier is shown in Fig. 8.2. 1.0 9IN / V 0.5 0 W W W –0.5 –1.0 Fig. 8.2 On Fig. 8.3, show the variation with time t of the output potential VOUT for time t = 0 to time t = t2. 15 9OUT / V 10 5 0 W W W –5 –10 –15 Fig. 8.3 [4] [Total: 9]

Mark scheme: 8 (a) (i) gain = voltage output / voltage input B1 [1] (ii) changes in VOUT M1 occur immediately when VIN changes A1 or changes in VIN (M1) result in immediate changes to VOUT (A1) [2] (b) 12 = 1 + R / (1.5 × 103) C1 R = 16.5 kΩ A1 [2] (c) straight line from (0,0) to (0.75t1, 9.0 V) B1 horizontal line from endpoint of straight line to t1 B1 +9 V to –9 V (or v.v.) at t1 B1 correct line to t2 B1 [4]

More questions on Potential difference and power

9 A magnetic field of flux density B is normal to face PQRS of a slice of a conducting material, as shown in Fig. 9.1. magnetic field flux density % S R Z FXUUHQW I P Q X Y Fig. 9.1 A current I in the slice is normal to face QRZY of the slice. The Hall voltage VH across the slice is given by the expression BI VH = . ntq (a) (i) State what is represented by the symbol n. ........................................................................................................................................... ...................................................................................................................................... [1] (ii) The symbol t represents the length of one side of the slice. Use letters from Fig. 9.1 to identify t. ...................................................................................................................................... [1] (b) (i) In general, the Hall voltage produced in a slice of a metal is very small. For a slice of the same dimensions with the same current and magnetic flux density, the Hall voltage produced in a semiconductor material is much larger. Suggest and explain why. ........................................................................................................................................... ........................................................................................................................................... ...................................................................................................................................... [2] (ii) In some semiconducting materials, electrons are mainly responsible for conduction. In other semiconducting materials, holes are mainly responsible for conduction. Suggest and explain the difference, if any, that conduction by electrons or by holes will have on the Hall voltage. ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... ...................................................................................................................................... [3] [Total: 7]

Mark scheme: 9 (a) (i) number density of charge carriers/free electrons or number per unit volume of charge carriers/free electrons B1 [1] (ii) PX or QY or RZ B1 [1] (b) (i) VH is inversely proportional to n B1 for semiconductors, n is (much) smaller than for metals B1 [2] (ii) magnetic field would deflect holes and electrons in same direction B1 (because) electrons are (–)ve, holes are (+)ve M1 so VH has opposite polarity/opposite sign A1 [3]

More questions on Density and pressure

10 Two coils P and Q are placed close to one another, as shown in Fig. 10.1. coil P coil Q V power supply Fig. 10.1 (a) The current in coil P is constant. An iron rod is inserted into coil P. Explain why, during the time that the rod is moving, there is a reading on the voltmeter connected to coil Q. ................................................................................................................................................... ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [2] (b) The current in coil P is now varied as shown in Fig. 10.2. current 0 0 W1 W2 WLPH Fig. 10.2 On Fig. 10.3, show the variation with time of the reading of the voltmeter connected to coil Q for time t = 0 to time t = t2. voltmeter reading 0 0 W1 W2 time Fig. 10.3 [4] [Total: 6]

Mark scheme: 10 (a) iron rod changes flux (density)/field B1 change of flux in coil Q causes induced e.m.f. B1 [2] (b) constant reading (either polarity) from time zero to near t1 B1 spike in one direction near t1 clearly showing a larger voltage M1 of opposite polarity A1 zero reading from near t1 to t2 B1 [4]

More questions on Electromagnetic induction

11 A bridge rectifier contains four ideal diodes A, B, C and D, as shown in Fig. 11.1. % input $ 9 ' & / 1 Fig. 11.1 The output of the rectifier is connected to a load L of resistance 2.4 kΩ. (a) On Fig. 11.1, mark with the letter P the positive terminal of the load. [1] (b) The variation with time t of the potential difference V across the input to the rectifier is shown in Fig. 11.2. 8 6 LQSXW 9 / V 4 2 0 W –2 –4 –6 –8 Fig. 11.2 Calculate the root-mean-square (r.m.s.) current in the load L. r.m.s. current = ..................................................... A [2] (c) The potential difference across the load L is to be smoothed using a capacitor. (i) On Fig. 11.1, draw the symbol for a capacitor, connected to produce smoothing. [1] (ii) The minimum potential difference across the load L with the smoothing capacitor connected is 3.0 V. On Fig. 11.2, sketch the variation with time t of the potential difference across the load L. [3] [Total: 7]

Mark scheme: 11 (a) point P shown at ‘lower end’ of load B1 [1] (b) Vr.m.s. = 6.0 / √2 = 4.24 V C1 Ir.m.s. = 4.24 / (2.4 × 103) = 1.8 × 10–3 A A1 [2] (c) (i) capacitor in parallel with load B1 [1] (ii) line from peak to curve at 3.0 V for either half- or full-wave rectified M1 correct curvature on line (gradient becoming more shallow) A1 line drawn as for full-wave rectified A1 [3]

More questions on Capacitors and capacitance

12 High-energy electrons collide with a metal target, producing X-ray photons. The variation with wavelength of the intensity of the X-ray beam is illustrated in Fig. 12.1. intensity 0 wavelength Fig. 12.1 (a) Explain why there is (i) a continuous distribution of wavelengths, ........................................................................................................................................... ........................................................................................................................................... ........................................................................................................................................... ...................................................................................................................................... [3] (ii) a sharp cut-off at short wavelength, ........................................................................................................................................... ........................................................................................................................................... ...................................................................................................................................... [2] (iii) a series of peaks superimposed on the continuous distribution of wavelengths. ........................................................................................................................................... ...................................................................................................................................... [1] (b) In the X-ray imaging of body structures, longer wavelength photons are frequently filtered out of the X-ray beam. (i) State how this filtering is achieved. ........................................................................................................................................... ...................................................................................................................................... [1] (ii) Suggest the reason for this filtering. ........................................................................................................................................... ...................................................................................................................................... [1] [Total: 8]

Mark scheme: 12 (a) (i) (X–ray) photon produced when electron/charged particle is stopped/accelerated (suddenly) B1 range of accelerations (in target) M1 hence distribution of wavelengths A1 [3] (ii) electron gives all its energy to one photon B1 electron stopped in single collision B1 [2] (iii) de-excitation of (orbital) electrons in target/anode/metal B1 [1] (b) (i) aluminium sheet/filter/foil (placed in beam from tube) B1 [1] (ii) (long wavelength X-rays) do not pass through the body B1 [1]

More questions on Energy and momentum of a photon

13 (a) Explain what is meant by gamma radiation (γ-radiation). ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [2] (b) A source of gamma radiation is placed a fixed distance away from a detector and counter, as illustrated in Fig. 13.1. WR FRXQWHU GHWHFWRU OHDG VKHHW [ VKLHOGLQJ VRXUFH Fig. 13.1 A sheet of lead of thickness x is placed between the source and the detector. The average count rate C, corrected for background, is recorded. This is repeated for different values of x. The variation with thickness x of ln C is shown in Fig. 13.2. 4.00 3.75 ln (& / s–1) 3.50 3.25 3.00 2.75 0 2 4 6 8 10 12 14 16 [ / mm Fig. 13.2 The absorption of gamma radiation in lead may be represented by the equation C = C0 e−μx where C0 is the count rate for x = 0 and μ is the linear attenuation (absorption) coefficient. Use Fig. 13.2 to determine the linear attenuation coefficient μ for this gamma radiation in lead. μ = .............................................. mm−1 [4] Question 13 continues on the next page. (c) The value of μ calculated in (b) is for gamma radiation in lead. Suggest and explain whether the value of μ for aluminium would be the same, greater or smaller. ................................................................................................................................................... ................................................................................................................................................... .............................................................................................................................................. [2] [Total: 8]

Mark scheme: 13 (a) (photons of) electromagnetic radiation M1 emitted from nuclei A1 [2] (b) line of best fit drawn B1 recognises µ as given by the gradient of best-fit line or ln C = ln C0 – µx B1 µ = 0.061 mm–1 (within ±0.004 mm–1, 1 mark; within ±0.002 mm–1, 2 marks) A2 [4] (c) aluminium is less absorbing (than lead) or gradient of graph would be less M1 so µ is smaller A1 [2]

More questions on Atoms, nuclei and radiation