A solid steel $(E=29{10}^3$ksi,$G=11{10}^3$ksi $)$ shaft supplies $175$ hp at A while rotating at $1800$ revolutions per minute $($rpm$).$ Gear B withdraws $100$ hp $,$ and gear C withdraws the remaining $75$ hp $.$ If the angle of twist $$ of gear C relative to A cannot exceed $0\mathrm{.}02$ radians, and the maximumallowable shear stress is $10$ ksi $,$ determine the required mirimum diameter of the shaft, to the nearest $\frac{1}{{16}^{de}}$ inch.