GATE2016-3-34

Question

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\theta _S$ is the twist and $\tau _S$  is the maximum shear stress in the solid shaft, whereas $\theta _H$ is the twist and $\tau _H$ is the maximum shear stress  in the hollow shaft. Which one of the following is 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 $\tau _S<\tau _H$