The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis is :

Options

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

Answer

D

Explanation

For disc `(5)/(4)mr^(2)=mk_(1)^(2)impliesk_(1)=sqrt((5)/(4))r`
For ring `(3)/(2)mr^(2)=mk_(2)^(2)" "k_(2)sqrt((3)/(2))r`
`therefore (k_(1))/(k_(2))=sqrt((5)/(4))/(sqrt((3)/(2)))=sqrt((10)/(12))=sqrt((5)/(6))`