Find the ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis in their planes.

Options

A. `2:3`
B. `2:1`
C. `sqrt(5):sqrt(6)`
D. `1:sqrt(2)`

Answer

C

Explanation

`I_(1)=(5M)/(4)R^(2)implies(5M)/(4)R^(2)=MK_(1)^(2)impliesK_(1)=sqrt((5)/(4))R`
`I_(2)=(3)/(2)MR^(2)implies(3MR^(2))/(2)=MK_(2)^(2)impliesK_(2)=sqrt((3)/(2))R`
`(K_(1))/(K_(2))=sqrt((5)/(4)xx(2)/(3))=sqrt((5)/(6))`