Some internal components for a novel torque wrench are shown below. The design premise is that the user applies torque at point C to a bolt or nut, and a gage detects angular deflection. When a certain amount of deflection occurs, a noise alerts the user to stop applying torque. In the interior of the wrench, the faces of the rod at D and E are fixed by surrounding support material not shown in the image. The axles are $4$ mm in diameter, with relevant lengths prescribed in the figure. The gears $($labelled A and B$)$ are $15$ mm and $10$ mm in diameter respectively. The collar of gear $B$ has an outer diameter of $8$ mm $.$ The gears, collars, and axles are all composed of a carbon steel with shear modulus $G=77$GPa.

For an applied torque $T=60N*m,$ determine the reaction torques at points D and E $.$