Question $3(6\mathrm{.}44)$

A circular shaft $AE$ of length $5a,$ diameter $d,$ and shear

modulus $G$ is welded to a support at end A and has a rigid

arm of length $b$ welded to its other end, E$.$ A pointer is

fastened to the shaft at $C.$ When the shaft is unloaded, the

pointer and the rigid arm are both horizontal, as shown in

$($a$).$ A weight $W$ is now hung on the end of the rigid arm

and, at the same time, moments $M_B$ and $M_D$ are applied to

the shaft at points B and D such that the pointer and the

rigid arm remain horizontal, as shown in $($b$).$ Find the

values of $M_B,$ and $M_D$ required to keep the pointer and

rigid arm horizontal when the weight $W$ is hung on the

arm.