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Center of mass and distance ratio

  1. Apr 20, 2007 #1
    how to show that the ratio of the distance between two particles from their centers of mass is the inverse of their masses? I tried but i found a way which can be possible if only we assume that they are constituted by a same number of small particles.
     
  2. jcsd
  3. Apr 20, 2007 #2
    Start with the definition of CM:
    [tex] x_{cm}={m_1\ell_1+ m_2\ell_2 \over m_1+m_2}[/tex]
    Then ask that the coordinate of the CM be zero. This is just a change in the position of the origin of x.
    Then compute de ratio of distances to the CM. Don't forget that now one of the distances in negative. See why?
     
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