(a) The ball bearings are to be selected for an application in which the radial load is 2 kN during 90 per cent of the time and 8 kN during the remaining 10 per cent. The shaft is to rotate at 150 rpm. Determine the minimum value of the basic dynamic load rating for 5000 hours of operation with not more than 10 per cent failures.
(b) The figure given below shows the state of stress at a point namely 30 N/mm2 tensile in X-direction. 20 n/mm2 tensile in Y-direction and a shears stress of 50 N/mm2. Find the location of the principal planes, principal stress and the maximum shear stress graphically or otherwise.
(c) (i) Derive a formula for increase in volume of a thin metallic sphere when it is subjected to an internal pressure p.
(ii) A thin spherical shell of copper has a diameter of 400 mm and a wall thickness of 2 mm and is just full of water at atmospheric pressure. Calculate the volume of water pumped in to raise the inside pressure to 1.5 N/mm2. The modulus of elasticity for copper is 1 X 105. K (Bulk Modulus) is 2.5 X 103 N/mm2 and Poisson’s ratio is 0.25.