Where Is the Center of Mass in a Plate with an Off-Center Hole?

[sweatband]

Homework Statement

A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The center C' of the smaller circle is a distance 0.80R from the center C of the larger circle. What is the position of the center of mass of the plate?

Homework Equations

Hints:
subtraction is to be used
answer expressed in terms of R

The Attempt at a Solution

I believe integration is required to solve this, but I do not know where to begin.

 

[sweatband]

If anyone knows of a link they could send me that could lead me in the right direction, please let me know!

 

[saket]

I believe integration is required to solve this, but I do not know where to begin.

On the other hand, I believe, if you know that centre of mass of a circle is at its centre, you do NOT need to worry about integration: addition (or, 'subtraction' as the hint says) will suffice!

HINT: The portion that has been cut out, you can assume that a disc of negative mass was superimposed in that portion! (Of course, of same magnitude of uniform mass density as the first one.)