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 ${}_y=145$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$)$

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