# Physics

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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.

• Physics -

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

• Physics -

How is it known that the mass of the cutout is centered at (2/3)R?

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