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

Answer

D

Explanation

Radius of gyration `K=sqrt((l)/(m))`
`K_("disc")=sqrt(((1)/(2)mR^(2)+mR^(2))/(m))=sqrt((3)/(2))R`
`K_("ring")=sqrt((mR^(2)+mR^(2))/(m))=sqrt(2)R`
`therefore (K_("disc"))/(K_("ring"))=(sqrt(3//2))/(sqrt(2))=(sqrt(3))/(2)`.