Two thin uniform rings made of same material and of radii `R` and `4 R` are joined as shown. The mass of smaller ring is `m`. Find the `M.I.` about an axis passing through the center of mass of system of rings and perpendicular to the plane.

Explanation

Here, `m_(1)=m,m_(2)=4m`
Location of the centre of mass from O
`X_(CM)=(mxxR+4m(2R+4R))/(m+4m)=5R`
A is CM of system of rings
`I_(A)=I_(1)+I_(2)={mR^(2)+m(5R-R^(2))}+{4m(4R)^(2)+4m(6R-5R)^(2)}`
`=mR^(2)[{1+16}+{64+4}]`
`I_(A)=85 mR^(2)`.