The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and a circular ring of the same radius about a tengential axis in the plane of the ring is

Options

A. `2:3`
B. `2:1`
C. `sqrt5:sqrt6`
D. `1:sqrt2`

Answer

C

Explanation

`I_(1)= (5M)/(4) R^(2) rArr (5M)/(4) R^(2)= MK_(1)^(2) rArr K_(1)= sqrt((5)/(4))R`
`I_(2)= (3)/(2) MR^(2) rArr (3MR^(2))/(2)= MK_(2)^(2) rArr K_(2)= sqrt((3)/(2))R`
`(K_(1))/(K_(2))= sqrt((5)/(4) xx (2)/(3)) = sqrt((5)/(6))`