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(I/m)`
`K_("disc") = sqrt((1/2mR^2+mR^2)/m)=sqrt(3/2)R`
`K_("ring")=sqrt((mR^2+mR^2)/(m))=sqrt2R`
`:. K_("disc")/(K_("ring"))=(sqrt3//2)/sqrt2 = sqrt3/2`