Physics - Elasticity Question with Solution | TestHub

The torque for a twist $\theta$ is $\tau =\frac{GJ\theta }{L}$.

Statement-2: at equal outer radius $R$, $J_h=\frac{\pi (R^4-r^4)}{2}<J_s=\frac{\pi R^4}{2}$.

So the hollow cylinder needs less torque for the same twist, and Statement-2 is false.

Statement-1: at equal mass and length, the hollow shaft has a larger radius and a larger $J$, so it can carry more torque. Statement-1 is true.

Answer: C.