9702_w23_qp_42
A paper of Physics, 9702
Questions:
10
Year:
2023
Paper:
4
Variant:
2
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1
Define the radian. The minute hand of a clock revolves at constant angular speed around the face of the clock, completing one revolution every hour. A small piece of modelling clay is attached to the hand with its centre of gravity at a distance L from the fixed end of the hand, as shown in . L free end face of clock modelling clay direction of revolution of minute hand minute hand fixed end Calculate the angular speed ω of the minute hand. ω = rad s–1 During a time interval of 1400 s, the centre of gravity of the piece of modelling clay in moves through a total distance of 0.44 m. Calculate the angle through which the minute hand moves in this time interval. angle = rad Determine distance L. L = m Calculate the magnitude of the centripetal acceleration of the piece of modelling clay. centripetal acceleration = m s–2 Use your answer in to explain why the variation with time of the magnitude of the force exerted by the minute hand on the piece of modelling clay is negligible as the minute hand undergoes one full revolution.
12. Motion in a circle  →  12.2. Centripetal acceleration
12. Motion in a circle  →  12.1. Kinematics of uniform circular motion
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2
Define gravitational potential at a point. The Moon may be considered to be an isolated uniform sphere of mass 7.3 × 1022 kg and radius 1.7 × 106 m. Calculate the gravitational potential at the surface of the Moon. Give a unit with your answer. gravitational potential = unit An isolated uniform spherical planet has gravitational potential φ at its surface. A particle of mass m is projected vertically upwards from the surface. The particle is given just enough kinetic energy to travel to an infinite distance away from the planet, escaping from the gravitational pull of the planet, without any additional work being done on it. Determine an expression, in terms of m and φ, for the gravitational potential energy EP of the particle at the surface of the planet. EP = Show that the speed v at which the particle is projected upwards from the surface of the planet is given by v = –2φ. A particle is moving upwards at the surface of the Moon. Use your answer in and the expression in to determine the minimum speed of this particle that will result in it escaping from the gravitational pull of the Moon. speed = m s–1 Hydrogen may be assumed to be an ideal gas. The mass of a hydrogen molecule is 3.34 × 10–27 kg. Calculate the root-mean-square (r.m.s.) speed of a hydrogen molecule in hydrogen gas that is at a temperature of 400 K. r.m.s. speed = m s–1 The surface of the Moon reaches temperatures of approximately 400 K when in direct sunlight. Use your answers in and to suggest a reason why the Moon does not have an atmosphere consisting of hydrogen.
13. Gravitational fields  →  13.4. Gravitational potential
5. Work, energy and power  →  5.2. Gravitational potential energy and kinetic energy
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4
An electron in a metal rod moves randomly about a mean position. When an alternating voltage is applied to the ends of the rod, the mean position can be considered to oscillate with simple harmonic motion along the axis of the rod. shows the variation with time t of the displacement x of the mean position from a fixed point on the axis of the rod. 0.1 0.2 0.3 0.4 x / 10–15 m t / μs Determine the amplitude of the oscillations. amplitude = m Determine the angular frequency of the oscillations. angular frequency = rad s–1 Use your answers in and to show that the maximum drift speed v0 of the electron is 1.1 × 10–7 m s–1. The rod has a cross-sectional area of 4.3 cm2 and contains a number density of conduction electrons (charge carriers) of 8.5 × 1028 m–3. All of the conduction electrons in the rod may be assumed to be oscillating in phase with, and with the same amplitude as, the oscillation shown in . Use the information in to calculate the magnitude I0 of the maximum current in the rod. I0 = A On , sketch the variation of the current I in the rod with time t between t = 0 and t = 0.40 μs. I I0 –I0 0.1 0.2 0.3 0.4 t / μs Use your answers in and to determine an expression for I in terms of t, where I is in A and t is in s. I = Determine the root-mean-square (r.m.s.) current in the rod. r.m.s. current = A
21. Alternating currents  →  21.1. Characteristics of alternating currents
9. Electricity  →  9.1. Electric current
17. Oscillations  →  17.1. Simple harmonic oscillations
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5
State Coulomb’s law. Two identical oil droplets are in a vacuum. The centres of the droplets are a distance of 3.8 × 10–6 m apart. The droplets have equal charge and exert an electric force on each other of magnitude 6.3 × 10–17 N. Determine the magnitude of the charge on each droplet. charge = C One of the oil droplets in is now placed between two horizontal metal plates, as shown in . + 1200 V 0 V 5.2 cm metal plates oil droplet (not to scale) A potential difference (p.d.) of 1200 V is applied between the plates, with the top plate at the higher potential. The oil droplet is stationary and in equilibrium. State the sign of the charge on the oil droplet. On , draw four lines to represent the electric field between the plates. The distance between the plates is 5.2 cm. Determine the mass of the oil droplet. mass = kg
18. Electric fields  →  18.5. Electric potential
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6
A capacitor C is charged so that the potential difference (p.d.) V across its terminals is 8.0 V. The capacitor is connected into the circuit of . R 8.0 V C The switch is initially open. The switch is closed at time t = 0. shows the variation of V with the charge Q on the plates of capacitor C as the capacitor discharges. V / V Q / μC Show that the energy stored in capacitor C at time t = 0 is 1.8 mJ. Determine the capacitance of capacitor C. Give a unit with your answer. capacitance = unit shows the variation with t of –ln  V 8.0 V. 1.0 2.0 t / s –ln V 8.0 V Show that, when t is equal to one time constant, the value of –ln  V 8.0 V is equal to 1.0. Determine the time constant τ of the circuit in . τ = s Calculate the resistance of resistor R. resistance = Ω
19. Capacitance  →  19.3. Discharging a capacitor
19. Capacitance  →  19.2. Energy stored in a capacitor
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7
A Hall probe containing a thin slice of semiconducting material is placed in a uniform magnetic field of flux density B. The largest faces of the slice are perpendicular to the magnetic field, as shown in . x semiconducting slice 5.4 A 5.4 A P Q magnetic field, flux density B The thickness x of the slice is 1.8 mm. The number density of charge carriers in the semiconducting material is 1.5 × 1016 m–3. A constant current of 5.4 A is passed through the slice between the shaded faces. The Hall voltage VH that is developed between the terminals PQ is recorded. shows the variation with time t of B. 0.02 0.04 0.06 0.08 t / s B / 10–6 T Show that, when B is equal to 4.0 × 10–6 T, the magnitude of VH is 5.0 V. On , sketch the variation of VH with t between t = 0 and t = 0.080 s. –2 – 4 –6 0.02 0.04 0.06 0.08 t / s VH / V The Hall probe in is replaced with a small flat coil that has 3000 turns. The cross-sectional area of the coil is 3.4 × 10–4 m2. The plane of the coil is perpendicular to the magnetic field. The electromotive force (e.m.f.) E induced between the terminals of the coil is recorded as B varies as shown in . Show that the magnitude of E at time t = 0.010 s is 2.0 × 10–4 V. On , sketch the variation of E with t between t = 0 and t = 0.080 s. –2 – 4 0.02 0.04 0.06 0.08 t / s E / 10–4 V
20. Magnetic fields  →  20.3. Force on a moving charge
20. Magnetic fields  →  20.5. Electromagnetic induction
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8
State what is meant by a photon. When the surface of a metal plate is illuminated with electromagnetic radiation, electrons are sometimes emitted from the metal. State the name of this phenomenon. It is observed that this phenomenon occurs only when the frequency of the electromagnetic radiation is greater than a certain minimum value, regardless of the intensity of the radiation. Explain how this observation provides evidence for the existence of photons. shows the variation of the maximum kinetic energy of the emitted electrons in with the frequency of the incident radiation. frequency maximum kinetic energy State the name of the quantity represented by: the gradient of the line in the y-intercept of the extrapolated line in .
22. Quantum physics  →  22.2. Photoelectric effect
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9
Fluorine-18 (18 9F) is a radioactive nuclide that is used as a tracer in positron emission tomography (PET scanning). Fluorine-18 decays to a nuclide of oxygen (O) according to 9F Q P X + R 8O. State what is meant by a tracer. State the symbol of the particle that is represented by X and the values of P, Q and R. X: P: Q: R: Explain how the radioactive decay of fluorine-18 results in the emission from the body of the gamma-ray photons that are detected during a PET scan. Explain how the detection of the gamma-ray photons is used to produce an image of the tissue being examined. The half-life of fluorine-18 is T. A patient is injected with amount of substance n of fluorine-18. Determine an expression for the initial value R0 of the rate R of production of gamma-ray photons by the tracer, in terms of n, T and the Avogadro constant NA. R0 = On , sketch the variation with time t of R. R0 R 0 T t
24. Medical physics  →  24.3. PET scanning
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10
State Wien’s displacement law. Identify any symbols that you use. A cosmology student observes the electromagnetic radiation received from a star in a galaxy. The student uses Wien’s law to estimate the surface temperature of the star, a standard candle to estimate the distance to the galaxy, and the Stefan–Boltzmann law to estimate the radius of the star. The student observes that the radiation from the star is redshifted. State what is meant by a standard candle. State the reason why the radiation from the star is redshifted. The true values of the quantities observed or estimated are those that are corrected to allow for redshift. However, the student does not correct for redshift. By placing one tick (3) in each row, complete Table 10.1 to indicate how the observations and estimates made by the student compare with the true values. Table 10.1 student’s uncorrected value too low the same too high wavelength of radiation surface temperature of star distance to star radius of star
25. Astronomy and cosmology  →  25.2. Stellar radii
25. Astronomy and cosmology  →  25.3. Hubble’s law and the Big Bang theory
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