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The planet Mars may be considered to be an isolated sphere of diameter 6.79 × 106 m with its mass of 6.42 × 1023 kg concentrated at its centre. A rock of mass 1.40 kg rests on the surface of Mars. For this rock, determine its weight, weight = N show that its gravitational potential energy is –1.77 × 107 J. Use the information in to determine the speed at which the rock must leave the surface of Mars so that it will escape the gravitational attraction of the planet. speed = m s–1 For Examiner’s Use The mean translational kinetic energy of a molecule of an ideal gas is given by the expression = 3 2kT where T is the thermodynamic temperature of the gas and k is the Boltzmann constant. Determine the temperature at which the root-mean-square (r.m.s.) speed of hydrogen molecules is equal to the speed calculated in . Hydrogen may be assumed to be an ideal gas. A molecule of hydrogen has a mass of 2 u. temperature = K State and explain one reason why hydrogen molecules may escape from Mars at temperatures below that calculated in .

15. Ideal gases  →  15.3. Kinetic theory of gases

5. Work, energy and power  →  5.2. Gravitational potential energy and kinetic energy

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For Examiner’s Use A resistance thermometer and a thermocouple thermometer are both used at the same time to measure the temperature of a water bath. Explain why, although both thermometers have been calibrated correctly and are at equilibrium, they may record different temperatures. State in what way the absolute scale of temperature differs from other temperature scales, what is meant by the absolute zero of temperature. The temperature of a water bath increases from 50.00 °C to 80.00 °C. Determine, in kelvin and to an appropriate number of significant figures, the temperature 50.00 °C, temperature = K the change in temperature of the water bath. temperature change = K

14. Temperature  →  14.2. Temperature scales

9. Electricity  →  9.3. Resistance and resistivity

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For Examiner’s Use Define simple harmonic motion. A horizontal plate is vibrating vertically, as shown in . vertical oscillations frequency 4.5 Hz cube, mass 5.8 g plate The plate undergoes simple harmonic motion with a frequency of 4.5 Hz and amplitude 3.0 mm. A metal cube of mass 5.8 g rests on the plate. Calculate, for the cube, the energy of oscillation. energy = J The amplitude of oscillation of the plate in is gradually increased. The frequency remains constant. At one particular amplitude, the cube just loses contact momentarily with the plate. State the position of the plate in its oscillation at the point when the cube loses contact. For Examiner’s Use Calculate this amplitude of oscillation. amplitude = m

17. Oscillations  →  17.1. Simple harmonic oscillations

17. Oscillations  →  17.2. Energy in simple harmonic motion

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For Examiner’s Use State two functions of capacitors in electrical circuits. 1. 2. Three uncharged capacitors of capacitance C1, C2 and C3 are connected in series, as shown in . C1 C2 C3 plate A A charge of +Q is put on plate A of the capacitor of capacitance C1. State and explain the charges that will be observed on the other plates of the capacitors. You may draw on if you wish. Use your answer in to derive an expression for the combined capacitance of the capacitors. For Examiner’s Use A capacitor of capacitance 12 μF is charged using a battery of e.m.f. 9.0 V, as shown in . S1 S2 9.0 V 12 μF 20 μF Switch S1 is closed and switch S2 is open. The capacitor is now disconnected from the battery by opening S1. Calculate the energy stored in the capacitor. energy = J The 12 μF capacitor is now connected to an uncharged capacitor of capacitance 20 μF by closing S2. Switch S1 remains open. The total energy now stored in the two capacitors is 1.82 × 10–4 J. Suggest why this value is different from your answer in .

19. Capacitance  →  19.2. Energy stored in a capacitor

19. Capacitance  →  19.1. Capacitors and capacitance

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For Examiner’s Use The components for a bridge rectifier are shown in . supply load Complete the circuit of by showing the connections of the supply and of the load to the diodes. Suggest one advantage of the use of a bridge rectifier, rather than a single diode, for the rectification of alternating current. State what is meant by smoothing, the effect of the value of the capacitance of the smoothing capacitor in relation to smoothing.

21. Alternating currents  →  21.2. Rectification and smoothing

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For Examiner’s Use Define the tesla. A charged particle of mass m and charge +q is travelling with velocity v in a vacuum. It enters a region of uniform magnetic field of flux density B as shown in . particle mass m, charge +q uniform magnetic field flux density B The magnetic field is normal to the direction of motion of the particle. The path of the particle in the field is the arc of a circle of radius r. Explain why the path of the particle in the field is the arc of a circle. Show that the radius r is given by the expression r = mv Bq . For Examiner’s Use A uniform magnetic field is produced in the region PQRS, as shown in . P Q S R X uniform magnetic field The magnetic field is normal to the page. At point X, a gamma-ray photon interaction causes two particles to be formed. The paths of these particles are shown in . Suggest, with a reason, why each of the paths is a spiral, rather than the arc of a circle. State and explain what can be deduced from the paths about 1. the charges on the two particles, 2. the initial speeds of the two particles.

20. Magnetic fields  →  20.3. Force on a moving charge

18. Electric fields  →  18.2. Uniform electric fields

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For Examiner’s Use An explanation of the photoelectric effect includes the terms photon energy and work function energy. Explain what is meant by a photon, work function energy. In an experiment to investigate the photoelectric effect, a student measures the wavelength λ of the light incident on a metal surface and the maximum kinetic energy Emax of the emitted electrons. The variation with Emax of 1 λ is shown in . –1 –2 –3 –4 λ 1 / 106 m–1 Emax / 10–19 J The work function energy of the metal surface is Φ. State an equation, in terms of λ, Φ and Emax, to represent conservation of energy for the photoelectric effect. Explain any other symbols you use. For Examiner’s Use Use your answer in and to determine 1. the work function energy Φ of the metal surface, Φ = J 2. a value for the Planck constant. Planck constant = J s

22. Quantum physics  →  22.2. Photoelectric effect

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For Examiner’s Use Radon-222 is a radioactive element having a half-life of 3.82 days. Radon-222, when found in atmospheric air, can present a health hazard. Safety measures should be taken when the activity of radon-222 exceeds 200 Bq per cubic metre of air. Define radioactive decay constant. Show that the decay constant of radon-222 is 2.1 × 10–6 s–1. A volume of 1.0 m3 of atmospheric air contains 2.5 × 1025 molecules. Calculate the ratio number of air molecules in 1.0 m3 of atmospheric air number of radon-222 atoms in 1.0 m3 of atmospheric air for the minimum activity of radon-222 at which safety measures should be taken. ratio =

23. Nuclear physics  →  23.2. Radioactive decay

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The resistance of a light-dependent resistor (LDR) is approximately 500 Ω in daylight. Suggest an approximate value for the resistance of the LDR in darkness. resistance = Ω An electronic light-meter is used to warn when light intensity becomes low. A light-dependent resistor is connected into the circuit of . R R – –9 V +9 V +2.5 V +4.5 V + P 1.7 kΩ red green The operational amplifier (op-amp) is ideal. The resistors R are to ensure that the light-emitting diodes (LEDs) do not over-heat. On , mark the polarity of the point P for the red LED to be emitting light. The LDR is in daylight and has a resistance of 500 Ω. State and explain which diode, red or green, will be emitting light. The intensity of the light decreases and the LDR is in darkness. State and explain the effect on the LEDs of this change in intensity.

9. Electricity  →  9.3. Resistance and resistivity

10. D.C. circuits  →  10.3. Potential dividers

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For Examiner’s Use 10 Explain the principles of the generation and detection of ultrasound waves.

24. Medical physics  →  24.1. Production and use of ultrasound

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For Examiner’s Use 11 Distinguish between sharpness and contrast in X-ray imaging. sharpness: contrast: A student investigates the absorption of X-ray radiation in a model arm. A cross-section of the model arm is shown in . muscle bone B B M M 4.0 cm 8.0 cm Parallel X-ray beams are directed along the line MM and along the line BB. The linear absorption coefficients of the muscle and of the bone are 0.20 cm–1 and 12 cm–1 respectively. Calculate the ratio intensity of emergent X-ray beam from model intensity of incident X-ray beam on model for a parallel X-ray beam directed along the line MM, ratio = For Examiner’s Use BB. ratio = State whether your answers in would indicate that the X-ray image is sharp, has good contrast.

24. Medical physics  →  24.2. Production and use of X-rays

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For Examiner’s Use 12 In a cellular phone network, a region is divided into a number of cells, each with its own base station. Suggest and explain two reasons why a region is divided into a number of cells. 1. 2. A passenger in a car is using a mobile phone as the car moves across several cells. Outline how it is ensured that the phone call is continuous.

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