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. `sqrt(3) : sqrt(4)`
B. `sqrt(5) : sqrt(6)`
C. `sqrt(6) : sqrt(5)`
D. `sqrt(4) : sqrt(3)`

Answer

B

Explanation

Radius of gyration of a circular disc about a tangential axis
`K_(1)=sqrt((I_(1))/(m_(1)))=sqrt(((5//4)m_(1)R^(2))/(m_(1)))=sqrt((5)/(4))R`

Radius of gyration of a circular ring about a tangential axis
`K_(2)=sqrt((I_(2))/(m_(2)))=sqrt(((3//2)m_(2)R^(2))/(m_(2)))=sqrt((3)/(2))RrArr(K_(1))/(K_(2))=sqrt((5)/(6))`.