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. `sqrt2:1`
B. `sqrt2:sqrt3`
C. `sqrt3:sqrt2`
D. `1:sqrt2`

Answer

D

Explanation

`MK_(1)^(2)=MR^(2)`
`K_(1)=R`
`MK_(2)^(2)=(MR^(2))/(2)`
`K_(2)=(R)/(sqrt2)`
`(K_(2))/(K_(1))=(sqrt2)/(R)=(1)/(sqrt2)`