The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis perpendicular to plane of disc or ring is

Options

A. `1:2`
B. `sqrt5:sqrt6`
C. `2:3`
D. `sqrt3:2`

Answer

D

Explanation

Radius of gyration, `K=sqrt((k)/(m))`
`K_("disc")=sqrt(((1)/(2)mR^(2)+mR^(2))/(m))=sqrt((3)/(2))R`
`K_("ring")=sqrt((mR^(2)+mR^(2))/(m))=sqrt2R`
`rArr" "(K_("disc"))/(K_("ring"))=(sqrt((3)/(2)))/(sqrt2)=(sqrt3)/(2)`