The solid steel shaft $AB$ has a $40$ mm diameter. The hollow aluminum shaft BC has a $60$ mm outside diameter, a $30$ mm inside diameter, and is bonded to the steel shaft at point $B$ and connected to a fixed support at point C$.$ The allowable shear stress of the steel is $85$ MPa and the allowable shear stress of the aluminum is $60$ MPa $.$ Length AB is $500$ mm $.$ Length BC is $600$ mm $.$

a$)$ Determine the largest torque T that can be applied as shown if the allowable stresses are not to be exceeded.

b$)$ If $T=500N-m,$ determine the rntation in degrees at points $A,B$ and C $.$