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Q.
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 $10 \sqrt{3} m$
JEE MainJEE Main 2022System of Particles and Rotational Motion
Solution:
$I =\frac{ m \ell^2}{12}= mk ^2 \Rightarrow k ^2=\frac{\ell^2}{12} $
$\Rightarrow k =\frac{\ell}{\sqrt{12}}=\frac{\ell}{2 \sqrt{3}}=\frac{10 \sqrt{3}}{2 \sqrt{3}}=5$
