A solid circular shaft of diameter d and length $$L$$ is fixed at one end and free at the other end. A torque t is applied at the free end. The shear modulus of the material is $$G.$$ The angle of twist at three free ends is

A hollow circular shaft has an outer diameter of $$100$$ $$mm$$ and a wall thickness of $$25$$ $$mm.$$ The allowable shear stress in the shaft is $$125$$ $$MPa.$$ The maximum torque the shaft can transmit is

The maximum shear stress in a solid shaft of circular cross-section having diameter subjected to a torque $$T$$ is $$\tau $$ . If the torque is increased by four times and the diameter of the shaft is increased by two times, the maximum shear stress in the shaft will be

The maximum and minimum shear stresses in a hollow circular shaft of outer diameter $$20$$ $$mm$$ and thickness $$2$$ $$mm,$$ subjected to a torque of $$92.7$$ $$N.m$$ will be