A uniform cylinder has radius `R` and length `L`. If the moment of inertia of this cylinder about an axis passing through its centre and normal to its circular face is `mg` equal to the moment of inertia of the same cylinder about an axis passing through its centre and normal to its length, then

Explanation

Moment of inertia of cylinder about an axis passing through centre and normal circular face `=(MR^(2))/2` Moment of inertia of cylinder about an axis passing through centre and its length `=M[(L^(2))/12+(R^(2))/4]`
But `(MR^(2))/2=M[(L^(2))/12+(R^(2))/4]`
`(R^(2))/2=(L^(2))/12+(R^(2))/4rArr(R^(4))/4=(L^(2))/12,`
`:. L=sqrt(3)R`