The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is: (2004)
Solution:
For disc about in-plane tangent, $I_d = \frac{5}{4}MR^2 \implies k_d = \frac{\sqrt{5}}{2}R$. For ring about in-plane tangent, $I_r = \frac{3}{2}MR^2 \implies k_r = \sqrt{\frac{3}{2}}R$. Ratio is $\sqrt{5}:\sqrt{6}$.
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