A solid steel $G=12700$ksi shaft with the diameter of $d=1\mathrm{.}625in.$ is subjected to torques $T_B=250lb.ft,T_C=350lb.ft,$ and $T_D=120lb.ft,$ acting in the directions shown in the figure. Assume $a=47in.,b=74in.,$ and $c=32in.$

Determine the rotation angle of pulley $C$ with respect to the support at $A.$

$0\mathrm{.}0379$ rad

$0\mathrm{.}0222$ rad

$0\mathrm{.}0135$ rad

$0\mathrm{.}0309$ rad

$0\mathrm{.}0347$ rad