physics
posted by arslan .
The center of mass and the moment of inertia of a 2D rigid body
A 2D rigid body shown in the figure2 has constant density ρ kg/m2. It is a thin circular disc of radius R centered at point P that contains a circular cavity centered at point Q. The distance PQ = R/3. Find the center of mass of the rigid body

I can't see your Fig. 2, but all you have to do is subract the moment of inertia of cavity, treating it as if it were a mass with the same density. Subtract it from the moment of inertia of the larger disc, treating it as having no hole. You may have to use the parallel axis theorem for moments of inertia about axes that do not pass through a center of symmetry.