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1

The mass M of a spherical planet may be assumed to be a point mass at the centre of the planet. A stone, travelling at speed v, is in a circular orbit of radius r about the planet, as illustrated in . r v planet stone Show that the speed v is given by the expression v =  GM r  where G is the gravitational constant. Explain your working. A second stone, initially at rest at infinity, travels towards the planet, as illustrated in . x planet V0 stone (not to scale) The stone does not hit the surface of the planet. Determine, in terms of the gravitational constant G and the mass M of the planet, the speed V0 of the stone at a distance x from the centre of the planet. Explain your working. You may assume that the gravitational attraction on the stone is due only to the planet. Use your answer in and the expression in to explain whether this stone could enter a circular orbit about the planet.

13. Gravitational fields  →  13.2. Gravitational force between point masses

13. Gravitational fields  →  13.4. Gravitational potential

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2

A constant mass of an ideal gas has a volume of 3.49 × 103 cm3 at a temperature of 21.0 °C. When the gas is heated, 565 J of thermal energy causes it to expand to a volume of 3.87 × 103 cm3 at 53.0 °C. This is illustrated in . 565 J 3.49 × 103 cm3 21.0 °C 3.87 × 103 cm3 53.0 °C Show that the initial and final pressures of the gas are equal. The pressure of the gas is 4.20 × 105 Pa. For this heating of the gas, calculate the work done by the gas, work done = J use the first law of thermodynamics and your answer in to determine the change in internal energy of the gas. change in internal energy = J Explain why the change in kinetic energy of the molecules of this ideal gas is equal to the change in internal energy.

16. Thermodynamics  →  16.2. The first law of thermodynamics

15. Ideal gases  →  15.2. Equation of state

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3

A microwave cooker uses electromagnetic waves of frequency 2450 MHz. The microwaves warm the food in the cooker by causing water molecules in the food to oscillate with a large amplitude at the frequency of the microwaves. State the name given to this phenomenon. The effective microwave power of the cooker is 750 W. The temperature of a mass of 280 g of water rises from 25 °C to 98 °C in a time of 2.0 minutes. Calculate a value for the specific heat capacity of the water. specific heat capacity = J kg−1 K−1 The value of the specific heat capacity determined from the data in is greater than the accepted value. A student gives as the reason for this difference: ‘heat lost to the surroundings’. Suggest, in more detail than that given by the student, a possible reason for the difference.

14. Temperature  →  14.3. Specific heat capacity and specific latent heat

8. Superposition  →  8.3. Interference

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4

A helium nucleus contains two protons. In a model of the helium nucleus, each proton is considered to be a charged point mass. The separation of these point masses is assumed to be 2.0 × 10−15 m. For the two protons in this model, calculate the electrostatic force, electrostatic force = N the gravitational force. gravitational force = N Using your answers in , suggest why there must be some other force between the protons in the nucleus, this additional force must have a short range.

18. Electric fields  →  18.3. Electric force between point charges

13. Gravitational fields  →  13.2. Gravitational force between point masses

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5

A Hall probe is placed a distance d from a long straight current-carrying wire, as illustrated in . Hall probe current-carrying wire 4.0 A X Y d The direct current in the wire is 4.0 A. Line XY is normal to the wire. The Hall probe is rotated about the line XY to the position where the reading VH of the Hall probe is maximum. The Hall probe is now moved away from the wire, along the line XY. On the axes of , sketch a graph to show the variation of the Hall voltage VH with distance x of the probe from the wire. Numerical values are not required on your sketch. VH x d The Hall probe is now returned to its original position, a distance d from the wire. At this point, the magnetic flux density due to the current in the wire is proportional to the current. For a direct current of 4.0 A in the wire, the reading of the Hall probe is 3.5 mV. The direct current is now replaced by an alternating current of root-mean-square (r.m.s.) value 4.0 A. The period of this alternating current is T. On the axes of , sketch the variation with time t of the reading of the Hall voltage VH for two cycles of the alternating current. Give numerical values for VH, where appropriate. VH / mV t T 2T –6 –4 –2 A student suggests that the Hall probe in is replaced with a small coil connected in series with a millivoltmeter. The constant current in the wire is 4.0 A. In order to obtain data to plot a graph showing the variation with distance x of the magnetic flux density, the student suggests that readings of the millivoltmeter are taken when the coil is held in position at different values of x. Comment on this suggestion.

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

20. Magnetic fields  →  20.4. Magnetic fields due to currents

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6

Explain the use of a uniform electric field and a uniform magnetic field for the selection of the velocity of a charged particle. You may draw a diagram if you wish. Ions, all of the same isotope, are travelling in a vacuum with a speed of 9.6 × 104 m s−1. The ions are incident normally on a uniform magnetic field of flux density 640 mT. The ions follow semicircular paths A and B before reaching a detector, as shown in . A B detector vacuum uniform magnetic field, flux density 640 mT Data for the diameters of the paths are shown in . path diameter / cm A B 6.2 12.4 The ions in path B each have charge +1.6 × 10−19 C. Determine the mass, in u, of the ions in path B. mass = u Suggest and explain quantitatively a reason for the difference in radii of the paths A and B of the ions.

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

18. Electric fields  →  18.2. Uniform electric fields

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7

Define the radian. A telescope gives a clear view of a distant object when the angular displacement between the edges of the object is at least 9.7 × 10−6 rad. The Moon is approximately 3.8 × 105 km from Earth. Estimate the minimum diameter of a circular crater on the Moon’s surface that can be seen using the telescope. diameter = km Suggest why craters of the same diameter as that calculated in but on the surface of Mars are not visible using this telescope.

25. Astronomy and cosmology  →  25.2. Stellar radii

12. Motion in a circle  →  12.1. Kinematics of uniform circular motion

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8

Light of wavelength 590 nm is incident normally on a surface, as illustrated in . surface light wavelength 590 nm The power of the light is 3.2 mW. The light is completely absorbed by the surface. Calculate the number of photons incident on the surface in 1.0 s. number = Use your answer in to determine the total momentum of the photons arriving at the surface in 1.0 s, momentum = kg m s−1 the force exerted on the surface by the light. force = N

22. Quantum physics  →  22.1. Energy and momentum of a photon

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9

Some water becomes contaminated with radioactive iodine-131 (131 53. The activity of the iodine-131 in 1.0 kg of this water is 460 Bq. The half-life of iodine-131 is 8.1 days. Define radioactive half-life. Calculate the number of iodine-131 atoms in 1.0 kg of this water. number = An amount of 1.0 mol of water has a mass of 18 g. Calculate the ratio number of molecules of water in 1.0 kg of water number of atoms of iodine-131 in 1.0 kg of contaminated water . ratio = An acceptable limit for the activity of iodine-131 in water has been set as 170 Bq kg−1. Calculate the time, in days, for the activity of the contaminated water to be reduced to this acceptable level. time = days

23. Nuclear physics  →  23.2. Radioactive decay

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10

State the function of a comparator circuit incorporating an operational amplifier (op-amp). An ideal op-amp is incorporated into the circuit of . +1.5 V 1.2 k1 2.4 k1 +5 V R G –5 V V IN + – On , draw a circle around the part of the circuit that is being used as an output device. Show that the potential at the non-inverting input of the op-amp is 1.0 V. The variation with time t of the potential VIN at the inverting input of the op-amp is shown in . potential / V –6 –4 –2 time t t 2 t 1 +1.0 VIN 1. On the axes of , draw the variation with time t of the output potential of the op-amp. 2. State whether each diode is emitting light or is not emitting light at time t1 and at time t2. At time t1, diode R will and diode G will . At time t2, diode R will and diode G will .

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

10. D.C. circuits  →  10.1. Practical circuits

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11

Distinguish between an X-ray image of a body structure and a CT scan. X-ray image: CT scan: Data for the linear absorption coefficient μ of X-ray radiation of energy 80 keV are given in . metal μ / mm−1 aluminium copper 0.46 0.69 A parallel X-ray beam is incident on a copper filter, as shown in . copper filter emergent beam incident beam intensity I0 The intensity of the incident beam is I0. Calculate the thickness of copper required to reduce the intensity of the emergent beam to 0.25 I0. thickness = mm An aluminium filter of thickness 2.4 mm is now placed in the X-ray beam, together with the copper filter in . Calculate the fraction of the incident intensity that emerges after passing through the two filters. fraction = Express your answer in as a gain in decibels (dB). gain = dB

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

24. Medical physics  →  24.3. PET scanning

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12

Two people, living in different regions of the Earth, communicate either using a link provided by a geostationary satellite or using optic fibres. Explain what is meant by a geostationary satellite. The uplink frequency for communication with the satellite is 6 GHz and the downlink has a frequency of 4 GHz. Explain why the frequencies are different. Comment on the time delays experienced by the two people when communicating either using geostationary satellites or using optic fibres. Explain your answer.

13. Gravitational fields  →  13.2. Gravitational force between point masses

8. Superposition  →  8.1. Stationary waves

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