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.
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?