$4.$ Consider a single crystal of BCC iron oriented such that a tensile stress is applied along a $[010]$ direction.

$($a$)$ Compute the resolved shear stress along a $(110)$ plane and in a $[\backslash (\backslash$overline$\{1\}11]\backslash )$ direction when a tensile stress of $52$ MPa is applied.

$($b$)$ If slip occurs on a $(110)$ plane and in a $[111]$ direction, and the critical resolved shear stress is $30$ MPa $,$ calculate the magnitude of the applied tensile stress necessary to initiate yielding.