Chapter 3.3, Problem 62P

A solid shaft and a hollow shaft are made of the same material and are of the same weight and length. Denoting by n the ratio c₁/c₂ show that the ratio Ts/T_h of the torque T_s in the solid shaft to the torque T_h in the hollow shaft is (a) $\sqrt{\left(1-n^2\right)}/\left(1+n^2\right)$ if the maximum shearing stress is the same in each shaft, (b) (1 - n²)/(1 + n²) if the angle of twist is the same for each shaft.