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Homework Help: The density within of sphere so that gravity is constant

  1. Dec 1, 2009 #1
    1. The problem statement, all variables and given/known data
    If the gravitational field vector g inside a sphere is independent of the
    distance from the center of the sphere r, how does the density ρ(r) of the
    sphere vary as a function of r?

    2. Relevant equations
    gauss' law for gravity: integrate g*da=4*pi*G integrate ρ(r) dv

    3. The attempt at a solution
    So far i have g=contant= (a/r^2) integrate 0 to r r^2 dr im not sure what to do next.
  2. jcsd
  3. Dec 2, 2009 #2


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    Science Advisor
    Gold Member

    If the field vector g inside is constant with respect to radii, then you can pull it outside the integral for Gauss's law as long as your gaussian surface is a sphere. So you get [tex]g\oint_{dS}dA = -4\pi GM[/tex] The integral is just the surface area of the sphere you have, so [tex]g(4\pi r^2)=-4\pi GM[/tex] Can you figure it out from there?
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