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  4. A rod is rotating about an axis passing through its centre and perpendicular to its length. The radius of gyration for the rod is

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Q. A rod is rotating about an axis passing through its centre and perpendicular to its length. The radius of gyration for the rod isPhysics Question Image

System of Particles and Rotational Motion

Solution:

As, moment of inertia of rod,
$I_{\text{ rod }}=\frac{M L^{2}}{12}$ ...(i)
Using radius of gyration, $I=M k^{2}$ ...(ii)
Comparing Eqs. (i) and (ii), we get
Radius of gyration, $k=L / \sqrt{12}$