$($b$)$ The gears attached to a solid steel shaft are subject to the torques shown in Figure Q$2.$ The shaft has a diameter of $60$ mm and the shear modulus is $\backslash ($ G$=75\backslash$mathrm$\{$GPa$\}\backslash ).$ Determine:

i$.$ The internal torques developed in segments $\backslash ($ A B$,$ B C$,$ C D $\backslash )$ and $\backslash ($ D E $\backslash )$; also draw the torque diagram

$(8$ marks$)$

ii$.$ The angle of twist of end $\backslash ($ A $\backslash )$ with respect to $\backslash ($ E $\backslash )$; ensure that the direction of rotation is also indicated

$(7$ marks$)$