Question 44 of 280

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be _____ $m.$ Given, the length of the rod is $10\sqrt{3}m$.

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Answer: 5

Moment of inertia of the rod about an axis perpendicular to its length and passing through the centre is $I=\dfrac{m{l}^{2}}{12}$.
Using the relation, $I=m{k}^{2}$, we have
$\Rightarrow {k}^{2}=\dfrac{{l}^{2}}{12} \Rightarrow k=\dfrac{l}{\sqrt{12}}=\dfrac{l}{2\sqrt{3}}=\dfrac{10\sqrt{3}}{2\sqrt{3}}=5m$