Three thin unifrom circular discs each of mass `M` and radius `R` are placed touching each other on a horizontal surface such that an equilateral triangle is formed, when the center of three discs are joined. Find the `M.I.` about an axis passing through the center of mass system of discs and perpendicular to the plane.

Explanation

The center of mass of system is at `O` (due to symmetry)
Distance between the center of mass of system `O` and the center of disc `d=2R//sqrt3` (side of equilateral triangle is `2R`)

`M.I.` of disc about its own axis `=(1)/(2)MR^(2)`
`M.I.` of disc about `O`
`I_(1)=(1)/(2)MR^(2)+Md^(2)=(1)/(2)MR^(2)+M((2R)/(sqrt3))^(2)`
`=(11MR^(2))/(6)`
`I_(0)=3I_(1)=(33MR^(2))/(6)`