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Determine the x-coordinate of the mass center of the homogeneous hemisphere

  1. Oct 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine the x-coordinate of the mass center of the homogeneous hemisphere with the smaller hemispherical portion removed?

    I know what the answer should be it's Xcm = 45/112 R
    2. Relevant equations

    The center of mass R of a system of particles is defined as the average of their positions, ri, weighted by their masses, mi


    3. The attempt at a solution
    dm = pi*p*(R^2 - x^2)
    and then doing the (integral of x*(dm/dx)*dx)/integral from 0 to R (dm/dx)*dx
    which finally gives me 3/2R but this is wrong. Please someone help thanks
     

    Attached Files:

  2. jcsd
  3. Oct 16, 2008 #2

    berkeman

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    Staff: Mentor

    It's a little hard to tell without the integral in Latex notation, but did you remember to remove the smaller hemisphere? Why is your integration from 0 to R? And why isn't it a triple integral?
     
  4. Oct 16, 2008 #3
    Yes I did remove smaller hemisphere from bigger which gave me 3/2R. I don't understand what you mean and what you are asking?
     
  5. Oct 16, 2008 #4

    berkeman

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    Staff: Mentor

    I mentioned Latex to help you post your equations in a format that is more readable. Look at the Latex Tutorial thread in the Learning Materials area of the PF:

    https://www.physicsforums.com/forumdisplay.php?f=151

    I mentioned the triple integral, because what you wrote looks like a 1-D integration, and it would seem that you need to integrate over the volume of the object, no?
     
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