A torque $T$ is applied at the free end $($point $A)$ to the $20$ mm diameter steel rod. The rod is $1500$ mm long and is fixed at end B $.$ Assuming the steel is elastoplastic with material parameters $T_y=145$MPa and ${}_y=1\mathrm{.}883{10}^{-3}$ rads. Determine $($a$)$ the torque $T$ when the angle of twist at A is $25$ degrees $($in N $-$m$)$

$($b$)$ the diameter of the elastic core of the shaft $($in mm$)$