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

A circular shaft shown in the figure is subject to torsion $$T$$ at two points $$A$$ and $$B.$$ The torsional rigidity of portions $$CA$$ and $$BD$$ is $$G{J_1}$$ and that portion $$AB$$ is $$G{J_2}$$. The rotations of shaft at points $$A$$ and $$B$$ are $${\theta _1}$$ and $${\theta _2}$$. The rotation $${\theta _1}$$ is