$1)$A solid steel bar of circular cross section has diameter d $=40$ mm$,$ length L $=1\mathrm{.}3$ m and shear modulus of elasticity G $=80$ GPa. The bar is subjected to torques T acting at the ends. If the torques have magnitude T $=340$ N$.$m$,$ what is the maximum shear stress in the bar? What is the angle of twist between the ends?

$2)$In the above problem, if the allowable shear stress is $42$ MPa and the allowable angle of twist is $2\mathrm{.}5$o$,$ what is the maximum permissible torque?