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. `sqrt(5) : sqrt(6)`
B. `1 : sqrt(2)`
C. `2 : 3`
D. `2 : 1`

Answer

A

Explanation

Moment of inertia of a circular disc about a tangential axis in the plane of disc
`I_(1) = MK_(1)^(2) = (5)/(4)MR^(2), K_(1) = sqrt((5)/(4))R`
Moment of inertia of a circular ring of same radius about a tangential axis in the plane of the ring is
`I_(2) = MK_(2)^(2) = (3)/(2)MR^(2)`
`K_(2) = sqrt((3)/(2))R`
`:. (K_(1))/(K_(2)) = (sqrt(5//4)R)/(sqrt(3//2)R) = sqrt((5)/(4) xx (2)/(3)) = sqrt((5)/(6)) = sqrt(5) : sqrt(6)`