maximum shear stress in the hollow shaft

Question

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length ad polar moment of inertia. Both are subjected to same torque. Here. θ_S is the twist and $\tau _{s}$ is the maximum shear stress in the solid shaft, whereas θ_H is the twist and $\tau _{H}$ is the maximum shear stress in the hollow shaft. Which one of the following TRUE?

(a) $\Theta _{S} = \Theta _{H} and \tau _{S} = \tau _{H}$

(b) $\Theta _{S} > \Theta _{H} and \tau _{S} > \tau _{H}$

(c) $\Theta _{S} < \Theta _{H} and \tau _{S} < \tau _{H}$

(d) $\Theta _{S} = \Theta _{H} and \tau _{S} < \tau _{H}$

Answer 1

Given two circular shafts made of same material, one solid (S) and one hollow (H)