The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and a circular ring of the same radius about a tengential axis in the plane of the ring is

Options

A. `2:3`
B. `2:1`
C. `sqrt5:sqrt6`
D. `1:sqrt2`

Answer

C

Explanation

Moment of inertia of a disc and circular ring about a tangential axis in their planes are respectively,
`l_(d)=(5)/(4)M_(d)R^(2) and l_(r)=(3)/(2)M_(r)R^(2)`
`"But "l=MK^(2)" or "K=sqrt((l)/(K))`
`therefore" "(K_(d))/(K_(r))=sqrt((l_(d))/(l_(r))xx(M_(r))/(M_(d)))`
`rArr" "(l_(d))/(l_(r))=sqrt(((5//4)M_(d)R^(2))/((3//2)M_(r)R^(2))xx(M_(r))/(M_(d)))`
`=sqrt((5)/(6))=sqrt5:sqrt6`