Ratio of Radii of Gyration of Disc and Ring – Rankers Physics

Ratio of Radii of Gyration of Disc and Ring

The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is: (2008)

$\sqrt{2}:\sqrt{3}$
$\sqrt{3}:\sqrt{2}$
$1:\sqrt{2}$
$\sqrt{2}:1$

Solution:

Radius of gyration $k = \sqrt{I/M}$. For a disc, $I = \frac{1}{2}MR^2 \implies k_d = R/\sqrt{2}$. For a ring, $I = MR^2 \implies k_r = R$. Ratio $k_d/k_r = 1/\sqrt{2}$.

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