Problem $10\mathrm{.}2$ A motor supplies sufficient power to the system shown so that the gears $C$ and $D$ provide torques of $800N*m$ and $550N*m,$ respectively, to machinery in a factory. Power shaft segments $(1)$ and $(2)$ are hollow steel tubes with an outside diameter of $d_0=60mm$ and an inside diameter $d_i=50mm.$ If the power shaft $[$i$.$e$.$ segments $(1)$ and $(2)]$ rotates at $40rpm,$ determine:

a$)$ the maximum shear stress in segments $(1)$ and $(2)$;

b$)$ the power $($in kW$)$ that must be provided by the motor as well as the rotation speed $($in rpm$)$; and

c$)$ the torque applied to gear $A$ by the motor.