The torques shown are exerted on pulleys $C,B,$ and $A.$ Knowing that the entire shaft is made of cast$-$iron $)=(140$GPa, determine the following:

$($a$)$ The shaft in which the maximum shearing stress occur and it magnitude.

$($b$)$ The angle of twist between A and $B,$ where the length $L_{AB}=L_{CD}=0\mathrm{.}4m.$

$($c$)$ The angle of twist between $B$ and $C,$ where the length $L_{BC}=0\mathrm{.}6m.$