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Linear Mass Density - Bars (Center of Mass)

  1. Dec 2, 2014 #1
    image.jpg 1. The problem statement, all variables and given/known data
    The 4 black bars have constant linear density. In terms of L, find the coordinate of the center of mass

    2. Relevant equations
    M0 X = summation of (MiXi)

    3. The attempt at a solution
    I understand most of the solution, except the answer key says one thing I don't get
    M/sqrt(2) at (L/4, L/4)
    and at (L/4, 3L/4).
    Why is there less mass in the middle of bar though the bar is uniform?
  2. jcsd
  3. Dec 2, 2014 #2
    M is the mass of a bar of length L. The diagonal of the square is L√2. Half the diagonal is L/√2. That's the length of each of the smaller little bars along the diagonals. So their masses must be M/√2.

  4. Dec 3, 2014 #3
    Thanks! That made a lot of sense.
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