$5-40$ A $20-$mm$-$diameter steel shaft, made of AISI $1035$ HR steel, transmits power while rotating at $400re\frac{v}{m}in.$ Assume any bending moments in the shaft to be relatively small compared to the torque. Determine how much power, in units of kW $,$ the shaft can transmit with a static factor of safety of $1\mathrm{.}5$ based on

$($a$)$ the maximum$-$shear$-$stress theory.

$($b$)$ distortion$-$energy theory.