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Find the ratio of the radii of gyration ...

Find the ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis in their planes.

Text Solution

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For rotation about a tangent in its plane, the radius of gyration of
(1) a disc, `k_(disc)=(sqrt5)/(2)R`
(2) a ring, `k_(ring)=sqrt(3/2)R`
`therefore (k_(disc))/(k_(ring))=(sqrt5)/(2)xxsqrt(2/3)=sqrt(5/8)`
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