Finding the Center of Mass in a Divided Square

[cmrgator]

Imagine a square with side length "a". Now, divide the square into 4 equal squares with side length "a/2". In the top righthand corner of the large square, a circle with radius "a/4" is cut out, which also removes the top corner piece. What is the new center of mass? (The origin is at the center of the large square). Thanks for your help!

 

[On Radioactive Waves]

Here is an easy way to think about it.

Cut the circle out of the remaining 3 quarters of the large square, now you have a symmetrical shape about both x and y axis. The center of mass is the center, so we can now ignore this part.

Now what is the center of mass of the 3 circles?

 

[Tom D]

Sorry, I don't see how that helps because of the cut out corner piece.
Anyway, even with the corner piece, I wouldn't know what to do.

 

[On Radioactive Waves]

Oops, I missed the part about the corner cut out...


I guess its back to x_bar y_bar in the first place then...

Well, it could still be done the way I was suggesting, don't know if its any easier though...but the point was to take out all area symmetrical about both axis, to simplify the problem.