$($b$)$ A cantilever circular solid bar is subjected to a clockwise torsional moment of $10$ kNm at point $B$ and an anti$-$clockwise torsional moment of $2$ kNm at its free end point $C$ as shown in Figure $Q\mathrm{.}2($b$).$ Given that the modulus of rigidity is $80$ GPa. Calculate:

$($i$)$ the maximum shear stress induced in each portion of the bar, i$.$e$.$ portions $AB$ and $BC$; and

$(6$ marks$)$

$($ii$)$ the angle of twist at its free end $C.$

$(6$ marks$)$