Physics
posted by James on .
5. A circular pizza of radius R has a circular piece of radius R/3 removed from one side. The center of mass of the pizza with the hole is at a distance of_____ from the center of mass of the original pizza.
A. R/20
B. R/2
C. R/30
D. R/3
E. R/12
The answer is E, but why is it E? Thank you in advance.

say mass is area (density would cancel)
original mass = pi R^2 with center at x = 0
mass of cutout = pi R^2/9 with center at x = (2/3)R
mass of remaining = 8 pi R^2/9 with center at x
8 pi R^2/9 * x + pi R^2/9 * 2R/3 = pi R^2 * 0
8 x =  2 R/3
x =  R/12 yes E 
How is it known that the mass of the cutout is centered at (2/3)R?