(c) If a spherical conductor of radius 12 cm has a charge of 1.6 x 10-7 C distributed uniformly on its surface; calculate the electric field: (i) Inside the sphere. (ii) At a point from the sphere 18cm

1. At a point from the sphere 18cm (0 mk)
2. In demonstrating the motion of a charged particle, students considered an electron projected with an initial velocity of 107 into a uniform electric field between two parallel plates of length 2 cm being at a distance of 1 cm apart. If the direction of the field was vertically downwards when the electron just missed the upper plate as it emerges from the field, evaluate the magnitude of electric field. (0 mk)
3. Two point charge +2q should be placed between two-point charges A and B of +2q and -4q respectively are situated 90 mm apart. Where should a point charge of -2q be placed so that it experiences no resultant electrostatic force? (0 mk)

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(c) (i) Calculate the force on the conductor carrying current of 5 A passing through it, when a vertical straight conductor of length 0.6 m is situated in a horizontal uniform magnetic field of 0.1 tesla. (ii) Determine the angle through which the conductor must be substituted in the vertical plane so that the force on the conductor is halved.

1. Determine the angle through which the conductor must be substituted in the vertical plane so that the force on the conductor is halved. (0 mk)
2. Describe the hysteresis loop for soft and hard steel with the aid of labelled sketches. (0 mk)
3. Above Curie temperature ferromagnetic material becomes paramagnetic. (0 mk)

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(c) A beam of  -particles is directed normally at a thin metal foil in an -scattering experiment. Briefly explain why; (i) most -particles pass straight through the foil? (ii) some  -particles are deflected through angles of more than 90o? (iii) multiple scattering of an individual  -particle is unlikely?

1. calculate the ionisation energy of an element, when the energy of the convergence limit line of that element is -1.6 eV and that of the first energy level is -10.4 eV. (0 mk)
2. determine the electric current flowing in the tube, when 0.5% of the energy obtained in 6 (b) (i) is transformed into X-rays and 600 W was produced. (0 mk)
3. multiple scattering of an individual  -particle is unlikely? (0 mk)

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(ii) Determine the width of the central maximum on a screen placed at a distance of 1 m from the slit, if the given slit width was 0.1 mm, and the slit was illuminated with a monochromatic light of wavelength of 5000

1. Account for a suction effect phenomenon based on Bernoulli’s Theorem. (4 mk)
2. A raindrop of radius 2 mm falls from a height of 500 m above the ground with decreasing acceleration to half its original height. If it attains its maximum terminal speed and moves with uniform speed thereafter, determine the work done by the gravitational force on the drop in the first and second of its journey. (0 mk)
3. A raindrop of radius 2 mm falls from a height of 500 m above the ground with decreasing acceleration to half its original height. If it attains its maximum terminal speed and moves with uniform speed thereafter, determine the work done by the gravitational force on the drop in the first and second of its journey. (6 mk)
4. Distinguish between static pressure and dynamic pressure as applied in laminar fluid flow. (4 mk)
5. Water is flowing steadily through a horizontal pipe of uniform cross-sectional area. If the velocity and pressure at a point where cross section area is 0.02 m2 are 2 m/s and 4 × 104 Nm-2, respectively, calculate the pressure at a point where the cross-sectional area is reduced to 0.01 m2. (0 mk)
6. Water is flowing steadily through a horizontal pipe of uniform cross-sectional area. If the velocity and pressure at a point where cross section area is 0.02 m2 are 2 m/s and 4 × 104 Nm-2, respectively, calculate the pressure at a point where the cross-sectional area is reduced to 0.01 m2. (6 mk)
7. Determine the rate of flow of glycerine of density 1.25 × 103 kgm3 through the cross section of a pipe if the radii at its ends and the pressure of a drop across its length are 0.1 m, 0.04 m and 10 N/m2, respectively. (0 mk)
8. Determine the rate of flow of glycerine of density 1.25 × 103 kgm3 through the cross section of a pipe if the radii at its ends and the pressure of a drop across its length are 0.1 m, 0.04 m and 10 N/m2, respectively. (6 mk)

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(i) Identify the necessary conditions for interference of light to occur. (ii) Explain briefly when Fraunhofer’s diffraction takes place.

1. Determine the number of beats per second heard by the observer (assuming there was no wind), when a whistle gave a sound of frequency of 500 Hz moving away with the velocity of 1.5 m/s from a stationary observer in a direction towards and perpendicular to a flat wall. (0 mk)
2. Determine the number of beats per second heard by the observer (assuming there was no wind), when a whistle gave a sound of frequency of 500 Hz moving away with the velocity of 1.5 m/s from a stationary observer in a direction towards and perpendicular to a flat wall. (5 mk)
3. Determine the width of the central maximum on a screen placed at a distance of 1 m from the slit, if the given slit width was 0.1 mm, and the slit was illuminated with a monochromatic light of wavelength of 5000 (5 mk)
4. Calculate the frequency of the note when a wire of length 140 cm and mass was stretched by means of a load of 16 kg. (5 mk)
5. Estimate the positions where two bridges were to be placed to divide the wire into three segments whose fundamental frequencies were in the ratio of 1:2:3. (5 mk)
6. Identify the necessary conditions for interference of light to occur. (2 mk)
7. Explain briefly when Fraunhofer’s diffraction takes place. (3 mk)

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State six assumptions that form the basic postulates of the kinetic theory of gases.

1. Explain why reducing the volume of a gas at constant temperature leads to an increase in pressure. (4 mk)
2. Deduce Avogadro’s law in terms of the kinetic theory of gases. (6 mk)
3. Explain the terms root mean square speed and mean speed of gas molecules. (4 mk)
4. Determine the root mean square speed of a hydrogen molecule at a given temperature of 27o C, using the Boltzmann constant (K = 1.38×10-23J/K). (6 mk)
5. State six assumptions that form the basic postulates of the kinetic theory of gases. (6 mk)

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