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I am looking for a proof of the following statement, known as Archimedes' Lemma:

If an object is divided into two smaller objects, the center of mass of the compound object lies on the line segment joining the centers of mass of the two smaller objects.

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    What's your definition of center of mass?2012-08-26
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    I think center of mass = center of gravity, which seems to be a more widespread name.2012-08-26
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    @DonAntonio: There is a distinction, but in uniform gravity fields they are the same point, hence often used interchangeably. The COG is the average position of the weight distribution, whereas the COM is the average mass distribution.2012-08-26

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