A motor driving a solid circular steel shaft transmits $$40$$ $$kW$$ of power at $$500$$ $$rpm$$. If the diameter of the shaft is $$40$$ $$mm,$$ the maximum shear stress in the shaft is ________ $$MP$$a.

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that 𝑟₃ > 𝑟₁ and 𝑟₄ > 𝑟₂ , and that the areas of the cross-sections are the same. J₁ and J₂ are the torsional rigidities of the bars on the left and right, respectively. The ratioJ₂/J₁ is

A rope brake dynamometer attached to the crank shaft of an $$I.C.$$ engine measures a brake power of $$10$$ kW when the speed of rotation of the shaft is $$400$$ rad/s. The shaft torque (in N-m) sensed by the dynamometer is ________

Consider a stepped shaft subjected to a twisting moment applied at $$B$$ as shown in the figure. Assume shear modulus, $$G=77$$ GPa. The angle of twist at $$C$$ (in degrees) is ________