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. `sqrt(5) : sqrt(6)`
D. `1 : sqrt(2)`

Answer

C

Explanation

Moment of inertia of a circular disc about a tangent in its own plane
`l_(1)=(5)/(4)" MR"^(2)`
Hence, `" "k_(1)=(sqrt(5))/(2)R`
Again moment of inertia of ring about a tangential axis in its own plane
`l_(2)=(3)/(2)" MR"^(2)`
Hence, `" "k_(2)=(sqrt(6))/(2)R`
`implies" "(k_(1))/(k_(2))=sqrt((5)/(6))`
`implies" "k_(1):k_(2)=sqrt(5):sqrt(6)`