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Center of gravity

  1. Apr 19, 2007 #1
    1. The problem statement, all variables and given/known data
    A unifrom disc A of radius 2m is cut as shown in the image. The cut out is also a disc of radius 1m. Find the distance of the two center of gravity before and after the paper disc is cut.

    [​IMG]
    2. Relevant equations

    x=m1x1/M+m2x2/M+......

    3. The attempt at a solution

    Mass of the disc is proportional to its area.
    so mass of disc A=2^2pi=4pi units
    mass of disc being cut out=1^2pi=pi units

    Let x be the distance between the two centers of gravity.
    (4pi-pi)(2-x)=(4pi)(2)-(2+1)(pi)
    x=0.333m

    This question is quite difficult for me. I don't have much confidence on my answer.:tongue2: May anyone try it?:smile:
     
    Last edited: Apr 19, 2007
  2. jcsd
  3. Apr 19, 2007 #2

    mezarashi

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    Homework Helper

    Your answer looks correct in my book.

    You assume the homogeneity of the disc, and thus mass is proportional to the area. You know that together, they produce a center of gravity balanced at the center of disc A, and your equations reflect that.
     
  4. Apr 19, 2007 #3
    I feel like my answer is not correct:frown:. I guess x should be about 0.5.
     
  5. Apr 19, 2007 #4
    well to check maybe you could use same methods with your new result and cut out identical hole in left half. I think it will end up in the middle again.
     
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