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

Answer

B

Explanation

(b) The radius of gyration is given by
`K = sqrt((I)/(M))`
For given problem `(K_(disc))/(K_(ring)) = sqrt((I_(disc))/(I_(ring))`…(i)
But `I_(disc)` (about its axis) `= (1)/(2) MR^2`
and `I_(ring)` (about its axis) `= MR^2`
where `R` is the radius of both bodies.
Therefore, Eq. (i) becomes
`(k_(disc))/(K_(ring)) = sqrt(((1)/(2) MR^2)/(MR^2)) = 1 : sqrt(2)`.