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`

Explanation

Disc: `I_(1)=(1)/(4)mr^(2)+mr^(2)=(5)/(4)mr^(2)=mk_(1)^(2)`
Ring: `I_(2)=(1)/(2)mr^(2)+mr^(2)=(3)/(2)mr^(2)=mk_(2)^(2)`
`(k_(1)^(2))/(k_(2)^(2))=(5//4)/(3//2)=(5)/(6)implies (k_(1))/(k_(2))=(sqrt5)/(sqrt6)`