QUESTION $2$

a$)$ A hollow circular shaft designed to have an inner diameter of $0\mathrm{.}7D{o}^{\text{;}}$ where $D{o}_0$ is an outer diameter.

i$)$ Determine the inner and outer diameters of the shaft if the maximum allowable shearing stress is $50\frac{N}{m}{m}^2$ and torque is $500kNm.$ Then, calculate the polar moment of inertia.

ii$)$ By using inner diameter calculated in $($i$),$ calculate the maximum shearing stress and a new torque, if the shaft is changed to solid circular shaft. The shaft is $1\mathrm{.}5m$ long with the twisted through an angle of $5.$ Take modulus of rigidity is $85$GPa.