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 .
A) 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.
B) Find the y-coordinate.
Please show work.
Figure is on the reply box.
Sorry, but I know that I asked this question before and @Irishboy123 greatly helped me ; but I want to understand the concept a little more.
Thank You.

Answer 1

I think that we have to apply the additivity property of the center of mass of an object

Answer 2

namely, if I call with X, and Y the x-coordinate and the y-coordinate of the center of mass of the uneaten pizza, then I can write:
\[\large \left\{ \begin{gathered}
0 = \frac{{\left( {3/4} \right)MX - 0.8M}}{M} \hfill \\
0 = \frac{{\left( {3/4} \right)MY - 0.8M}}{M} \hfill \\
\end{gathered} \right.\]

Answer 3

where M is the mass of the whole pizza

Answer 4

Thank you, but I tried that way but I am still getting the wrong answer. The M's cancel out an I get 1.06 for both; but it is still telling me that my answer is wrong.
Any other way of doing this problem?

Answer 5

Of course, there is another method. Such method, employs the integral calculus, and our pizza can be viewed as a disk whit a mass density.
Using that method, we can find that the x-coordinate, and y-coordinate of the partially eaten pizza are:
x=-0.64 inches
y=-0.64 inches
Please note that those values, are approximate values. The exact values are:
\[\large x = y = - \frac{2}{\pi }\]

So, we can conclude that the requested coordinates, are:
X=-0.64 inches
Y=0.64 inches

Answer 6

.