The solid shaft of radius r is subjected to a torque T . Determine the radius r’ of the...

The solid shaft of radius r is subjected to a torque T . Determine the radius r’ of the inner core of the shaft that resists one-quarter of the applied torque ( T/4). Solve the problem two ways: (a) by using the torsion formula, (b) by finding the resultant of the shear-stress distribution.