Assertion : A hollow shaft is found to be str | vedclass

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Question

(A) The torsional rigidity of a shaft is given by $C = \frac{\eta J}{L}$, where $\eta$ is the modulus of rigidity, $J$ is the polar moment of inertia,

Vedclass · Accepted Answer

If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.

Vedclass · Answer

(A) The torsional rigidity of a shaft is given by $C = \frac{\eta J}{L}$, where $\eta$ is the modulus of rigidity, $J$ is the polar moment of inertia, and $L$ is the length. For a given torque $	au$, the angle of twist $	heta$ is $	heta = \frac{	au L}{\eta J}$. For a hollow shaft, the material is distributed further from the axis, which increases the polar moment of inertia $J$ for the same mass. Since $J_{hollow} > J_{solid}$ for the same mass and length, the torque required to produce a specific twist $	heta$ is higher for the hollow shaft. Therefore, the hollow shaft is stronger in torsion, and the reason correctly explains the assertion.

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