Two circular disc having radius R and mass density `sigma` and `2sigma` respectively are placed as shown in figure. Then find out the position of COM of the system.

Explanation

Mass of disc A `m_(A) = sigmapiR^(2)`
Mass of disc B `m_(B) = 2sigmapiR^(2)`
Due to symmetry the COM of disc A lie at point O and COM of disc B lie at point O'. So we realize the above problem in a following way

Centre of mass due to both the disc lie at point C (assume),
having distance x from `m_(A)`
`hArrx=(m_(B)(2R))/(m_(A)+m_(B))` , `x=(2sigmapiR^(2)(2R))/(sigma(piR^(2)+2piR^(2)))` , `x=(4R)/3`
So the centre of mass lie in the disc B having distance `(4R)/3` from O.