Figure $0\mathrm{.}5(a)$

$($b$)$ A round steel shaft ABC is shown in Figure Q$\mathrm{.}5($b$).$ The portion $BC$ is $600$ mm long and $35$ mm in diameter. The portion $AB$ is $900$ mm long and $50$ mm in diameter, but a $30$ mm diameter hole has been bored from fixed end, $A,$ to a depth of $300$ mm $.$ The shaft carries a pure torque, $T,$ applied at the free end, $C,$ and has been designed so that the maximum torsional shear stress due to torsion is $90\frac{N}{m}{m}^2.$ Determine the angle of twist at $C$ resulting from the applied torque, $T.$ The modulus of rigidity may be taken as $80k\frac{N}{m}{m}^2.$

$(13$ marks$)$

$($All dimensions are in mm$)$

$($ans $3\mathrm{.}04$deg$)$