Finding the Center of Gravity of a Pizza with a Missing Slice

[Honda47]

Here is my question I'm not sure even how to come up with the answer:

A circular pizza of radius R has a circular piece of radious R/2 removed from one side. The center of gravity has moved from C to C' along the x axos. Show that the distance from C to C' is R/6. Assume the thickness and density of the pizza are uniform throughout.

If anyone could give me some pointers they would be greatly appreciated.

 

[Silimay]

Find the center of mass of the pizza (in the center, obviously) and then find the center of mass of the removed piece.

Xcom = (m1x1 + m2X2) / (total mass)

If the pizza has density d, then the total area must be R^2*pi - (R/2)^2*pi. This goes in the denominator. Now you simply find the center of mass of the removed piece, which should be (R/2)^2*pi. Multiply this by R/2 (the distance to the center). I hope that helps some.

 

[Doc Al]

This may help: https://www.physicsforums.com/showthread.php?t=55076