Find Center of Gravity Distances for Cut Discs

[crossfacer]

Homework Statement

A unifrom disc A of radius 2m is cut as shown in the image. The cut out is also a disc of radius 1m. Find the distance of the two center of gravity before and after the paper disc is cut.

http://crossfacer.com/circle.jpg

Homework Equations

x=m1x1/M+m2x2/M+...

The Attempt at a Solution

Mass of the disc is proportional to its area.
so mass of disc A=2^2pi=4pi units
mass of disc being cut out=1^2pi=pi units

Let x be the distance between the two centers of gravity.
(4pi-pi)(2-x)=(4pi)(2)-(2+1)(pi)
x=0.333m

This question is quite difficult for me. I don't have much confidence on my answer. May anyone try it?

 

[mezarashi]

Your answer looks correct in my book.

You assume the homogeneity of the disc, and thus mass is proportional to the area. You know that together, they produce a center of gravity balanced at the center of disc A, and your equations reflect that.

 

[crossfacer]

Your answer looks correct in my book.

You assume the homogeneity of the disc, and thus mass is proportional to the area. You know that together, they produce a center of gravity balanced at the center of disc A, and your equations reflect that.

I feel like my answer is not correct. I guess x should be about 0.5.

 

[denverdoc]

well to check maybe you could use same methods with your new result and cut out identical hole in left half. I think it will end up in the middle again.