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 ________

Two solid circular shafts of $${{R_1}}$$ and $${{R_2}}$$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $${\tau _1}$$ and $${\tau _2}.$$ If $${{{R_1}} \over {{R_2}}} = 2,$$ then $${{{\tau _1}} \over {{\tau _2}}}$$ is _______.

A solid circular shaft of diameter $$d$$ is subjected to a combined bending moment, $$M$$ and torque, $$T.$$ The material property to be used for designing the shaft using the relation $${{16T} \over {\pi {d^3}}}\sqrt {{M^2} + {T^2}} $$

For a circular shaft of diameter $$'d'$$ subjected to torque $$T,$$ the maximum value of the shear stress is