The elastic torsion formula can be rearranged to determine the allowable torque $\mathrm{T}$ that causes a maximum shearing stress of $50 \mathrm{MPa}$. The maximum shearing stress occurs on the outermost surface of the shaft; therefore, $\mathrm{c}=20 \mathrm{mm}$:

$\mathrm{\tau }=\frac{\mathrm{Tc}}{\mathrm{J}} \therefore \mathrm{T}=\frac{\mathrm{\tau J}}{\mathrm{c}}$