If `k_(1)` is radius of gyration of a circular disc about a tangent perpendicular to plane of disc and `k_(2)` is radius of gyration of a circular ring of same size as disc about any diameter, what is the value of `K_(1)^(2)//K_(2)^(2)` ?

Answer

`(3)`

Explanation

Moment of inertia of circular disc about a tangent perpendicular to the plane of disc
`I_(1) = MK_(1)^(2) = (3)/(2)MR^(2) , K_(1)^(2) = (3)/(2)R^(2)`
Again, moment of inertia of circular ring of same size as disc about any diameter,
`I_(2) = M'K_(2)^(2) = (1)/(2)M'R^(2)`
`K_(2)^(2) = (1)/(2)R^(2) :. (K_(1)^(2))/(K_(2)^(2)) = (3//2R^(2))/(1//2R^(2)) = 3`