The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is.

Options

A. `sqrt2 : sqrt3`
B. `sqrt3:sqrt2`
C. `1:sqrt2`
D. `sqrt2:1`

Explanation

For circular disc. For circular ring.
`MK _(1) ^(2) = ( MR ^(2))/( 2) MK _(2) ^(2) = MR ^(3)`
`implies K _(t) = (R)/(sqrt2)implies K _(2) = R`
`So, (K _(1))/( K _(2)) =(R//sqrt2)/(R) = (1)/(sqrt2)`