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

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(B) For a circular disc of mass $M$ and radius $R$,the moment of inertia about an axis in its plane and tangent to it is $I_1 = \frac{5}{4}MR^2$.Since

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$\sqrt{5}:\sqrt{6}$

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(B) For a circular disc of mass $M$ and radius $R$,the moment of inertia about an axis in its plane and tangent to it is $I_1 = \frac{5}{4}MR^2$.Since $I = MK^2$,the radius of gyration $K_1 = \sqrt{\frac{I_1}{M}} = \sqrt{\frac{5}{4}}R = \frac{\sqrt{5}}{2}R$.For a circular ring of mass $M$ and radius $R$,the moment of inertia about an axis in its plane and tangent to it is $I_2 = \frac{3}{2}MR^2$.The radius of gyration $K_2 = \sqrt{\frac{I_2}{M}} = \sqrt{\frac{3}{2}}R$.The ratio of the radii of gyration is $\frac{K_1}{K_2} = \frac{\sqrt{5}/2}{\sqrt{3/2}} = \sqrt{\frac{5}{4} 	imes \frac{2}{3}} = \sqrt{\frac{5}{6}} = \frac{\sqrt{5}}{\sqrt{6}}$.

The ratio of the radius of gyration of a circular disc about an axis in its plane and tangent to it,to the radius of gyration of a circular ring about an axis in its plane and tangent to it is .........

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