Center of Mass Problem - Circle with Hole

Because Object X is symmetrical along the x-axis, the Center of Mass must lie over the x-axis.

In order to find our center of mass, we can treat our hole as another plate with negative mass. We will call our hole object D.

So, our center of mass is the center of mass of our whole circle and object D.

Or:

Because the center of mass of a regular circle is , . As a result, our equation can be:

Assuming the plate is of uniform density and thickness, we can use the area equations:

So our answer is: