(b) What are the conditions for a body to execute simple harmonic motion?
(ii) A particle moving with simple harmonic motion has period of 8.0 seconds and amplitude of 5.0m. What is the speed of the particle when it is 3.0m from the centre of its motion and its maximum acceleration?
(b) (i) An object of mass 4kg is whirled in a vertical circle of radius 2m with a speed of 5ms-1 Calculate the maximum and minimum tension in the string connecting the object and the centre of the circle.
(ii) Find the angle of banking necessary for a corner of radius 80m if cars are to travel round this corner at a speed of 120km/h without relying on the frictional forces.
5. (a) (i) Briefly explain what it means by thermal conduction and define the coefficient of thermal conductivity.
(ii) Ice cubes of mass 5.0g at OOC are placed inside a spherical container having an outside diameter of 40cm, 2mm thick and of thermal conductivity 5.0 x 10-4 WmIR-I . How long will it take for all the ice cubes to melt if the room temperature is 300C?
(b) Two metal rods A and B of lengths 40cm and 80cm respectively having the same cross sectional area of 10cm2are joined end to end. If the composition is perfectly lagged and the free end of A is fixed at 1000C while that of B is pressed to a point at OOC. Determine:
(i) The junction temperature of the two metal rods;
(ii) The quantity of heat that flows per minute in steady state. (Thermal Conductivities of rods A and B are 360 and 80Wm-1K-1 respectively).
(ii) What changes take place in the total energy radiated by the black body and in the energy distribution among the wavelengths radiated as its temperature rises? (Illustrate using suitable graphs). Explain how the information of the changes that take place in the total energy radiated could be obtained from the graph.
(b) A copper sphere with a black surface and radius 30mm is cooled to -730C and placed inside an enclosure at a temperature of 270C. Calculate the rate of temperature rise of the surface of the sphere. (Assume the sphere is a black body).
(ii) A capacitor of capacitance 300gF is connected in parallel with another capacitor of unknown capacitance C. The combination discharges through a resistor of 3600 with a time constant of 180 seconds. Calculate the value of unknown capacitance C.
(b) A standard cell of e.m.f of 1.0186V gives a balance length at 51.2cm on a potentiometer. Ifthe potential drop (p.d) across a standard resistor of 100 in the circuit gives a balance length at 78.4cm. What is the current in the circuit?
(ii)An a-particle has a mass of 6.68 x 1027kg and charge of +2e. Two a-particles are situated at a distance of 1.5 x 10Ilm apart in vacuum. How does the electrostatic force compare with the gravitational attraction between them?
(b) Point charges each of +2 x 10 'C are placed at each of the three corners of a square of side 0.20m. What would be the magnitude and direction of the resultant force on another point charge of -1 x 1019C If it is located at the: