The ratio of the radius of gyration of a thin | vedclass

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(A) The radius of gyration $k$ is given by the formula $k = \sqrt{\frac{I}{m}}$,where $I$ is the moment of inertia and $m$ is the mass.For a thin unif

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$\sqrt{2}: 1$

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(A) The radius of gyration $k$ is given by the formula $k = \sqrt{\frac{I}{m}}$,where $I$ is the moment of inertia and $m$ is the mass.For a thin uniform disc of mass $m$ and radius $R$:$1$. The moment of inertia about an axis passing through its centre and normal to its plane is $I_1 = \frac{mR^2}{2}$.$2$. The moment of inertia about its diameter is $I_2 = \frac{mR^2}{4}$.Let $k_1$ and $k_2$ be the radii of gyration corresponding to $I_1$ and $I_2$ respectively.Then,$\frac{k_1}{k_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{\frac{mR^2 / 2}{mR^2 / 4}} = \sqrt{\frac{4}{2}} = \sqrt{2} = \sqrt{2}: 1$.

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is

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