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  4. The radius of gyration of an uniform rod of length l about an axis passing through one of its ends and perpendicular to its length is

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Q. The radius of gyration of an uniform rod of length $l$ about an axis passing through one of its ends and perpendicular to its length is

System of Particles and Rotational Motion

Solution:

Moment of inertia of rod of mass $M$ and length $l$ about its axis passing through one of its ends and perpendicular to it is
$I = \frac{1}{3} Ml^2$
As $I = Mk^2$ where $k$ is the radius of the gyration
$\therefore Mk^2 = \frac{1}{3}Ml^2$ or $k = \frac{l}{\sqrt 3}$