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

The ratio of the radii of gyration of a circular disc and a circular r

1.	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
Answer» `1:2` `sqrt(5) : sqrt(6)` `2:3` `(sqrt(3))/(2)` Solution :Radius of GYRATION,`K=sqrt((I)/(m))` `K_("DISC")=sqrt(((1)/(2)mR^(2)+mR^(2))/(m))=sqrt((3)/(2))R` `R_("ring")=sqrt((mR^(2)+mR^(2))/(m))=sqrt(2)R` `:. (K_("disc"))/(K_("ring"))=(sqrt(3//2))/(sqrt(2))=(sqrt(3))/(2)`.