A solid steel shaft of 200 mm diameter transmits 5MW at 500 rev/min. It is proposed to alter the horsepower to 7 MW and the speed to 440rev/min and to replace the solid shaft by a hollow shaft made of the same type of steel but having only 80 % of the weight of the solid shaft. The length of both shafts is the same and the hollow shaft is to have the same maximum shear stress as the solid shaft. Find (a) the ratio between the torque per unit angle of twist per metre for the two shafts; (b) the external and internal diameters for the hollow shaft.