Question

Physics Help Please:
The location of the center of mass of the partially eaten, 12-inch diameter pizza shown in the figure (Figure 1) is Xcm = - 0.80in
and Ycm = -0.80in .
Assuming each quadrant of the pizza to be the same, find the center of mass of the uneaten pizza above the x axis (that is, the portion of the pizza in the second quadrant). Find the x-coordinate.
Express your answer using two significant figures.
Please show work.
Picture is posted on reply section.

Answer 1

I kept getting -2 because my equation was the following xcm=[M(-6)+M(0)+M(0)]/3M

Answer 2

there are a billion ways to do this, and none of them that easy to explain in this interface. however, in the above diagram we balance the pizza across the diagonal and we wonder why it should balance once the eaten bit is added back in.

we use the symmetry of the circle to its fullest extent and we can tell just how far from the origin the centre of mass of the eaten bit must be as we know its mass relative to the remaining parts.