Question

If two cylinders (one hollow and other solid) of same length, mass, and material are given, then, to twist the cylinders through the same angle:

• A. More torque is needed for the hollow cylinder than the solid one
• B. More torque is needed for the solid cylinder than the hollow one
• C. Couple per unit twist for solid cylinder will be more than the hollow one
• D. Couple per unit twist for solid as well as hollow cylinders will be the same

Hint:

A hollow cylinder has a larger moment of inertia than a solid one of the same mass.

Answer 1

The Correct Option is A

The torsional rigidity is given by:
\[ C = \frac{G J}{L} \] where \( J \) is the polar moment of inertia. For the same mass, the hollow cylinder has a larger \( J \) than the solid one, meaning it requires more torque to achieve the same twist.