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Finding mass of sphere with density

  1. Feb 19, 2013 #1
    my work, asking about Q3

    A solid ball of radius a has density given by (2a-p) where p = sqrt(x^2 + y^2 + z^2). Determine its mass.

    a) I think it's properly setup by converting to spherical, still iffy if (2a-p)=(2p-p)=p

    b) What did I just find and how do I then get mass?


    Thanks-a-centillion if you reply, this isn't homework, but is part of a practice midterm.
     
  2. jcsd
  3. Feb 19, 2013 #2

    Dick

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    (2a-p)=p is only true where a=p. That's on the outside of your sphere. On the inside it's just (2a-p). Integrate that.
     
  4. Feb 21, 2013 #3
    If you take the integral of (2a-p) it should work.
    Remember the mass is the integral of the density so the boundaries are p^2sin(phi)dp(dtheta)(dphi)
    The boundary conditions are:
    phi: 0... pi
    theta: 0...2pi
    p: 0...a

    So, triple integral(2a-p)p^2sinphi(dpdthetadphi)

    Sorry, I don't know how to make symbols on here yet but hope this helps!
     
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