A circular pizza of radius R has a circular piece of radius R/3 removed from one side,as shown in the figure.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

Question

A circular pizza of radius R has a circular piece of radius R/3 removed from one side,as shown in the figure.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

Quizplus · Accepted Answer

The center of mass of the original pizza is at the center of the circle, since it has uniform density. 
For the pizza with the hole, we can treat it as the difference between two circles: a full circle of radius R, and a smaller circle of radius R/3. 
Using the formula for the center of mass of two overlapping circles, we can find that the center of mass of the pizza with the hole is located at a distance of (4R/3pi)/(2R/pi) = 2R/3 from the center of the circle, on the line passing through the centers of the two circles. 
The distance between the two centers of mass is therefore R - 2R/3 = R/3.

A Circular Pizza of Radius R Has a Circular Piece