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  4. Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

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Q. Find ratio of radius of gyration of a disc and ring of same radii at their tangential axis in plane.

JIPMERJIPMER 2018System of Particles and Rotational Motion

Solution:

For disc
$MK^{2}_{1}=\frac{5}{4}MR^{2}$
$K_{1}=\frac{\sqrt{5}}{2}R$
$MK^{2}_{2}=\frac{3}{2}MR^{2} \Rightarrow K_{2}=\sqrt{\frac{3}{2}}R$
So, $\frac{K_{1}}{K_{2}}=\frac{\sqrt{5}\,\,\sqrt{2}}{2\,\,\sqrt{3}}=\sqrt{\frac{5}{6}}$

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