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Homework Help: Density of a Sphere

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data

    The density of a sphere of radius R as a function of distance from the centre r is ρ(r) = ρ0(1 − r/R)
    What is the mass of the sphere in terms of ρ0 and R?

    2. Relevant equations

    Volume of a Sphere=(4/3)piR3


    3. The attempt at a solution

    I'm somewhat confused by the question. To my understanding, I can determine the mass of the sphere by integrating from 0 to radius R. I would consider a spherical shell a distance r from the center and of thickness dr. Thus I integrate from 0 to R and get something like 4pir2(1-r/R)ρ(r)dr, which is the mass of the sphere. But I'm not sure if that's what is needed. Any ideas?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 18, 2010 #2

    rl.bhat

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    Homework Helper

    dm = 4pir2(1-r/R)ρ(r)dr
    Complete the integration. So
    m = 4*pi*rho* intg(r^2*dr - r^3*dr/R) from zero to R.
     
  4. Jan 19, 2010 #3
    Huh, I'm not quite sure how the integration with (1-r/R) works...R would be the radius, and r would be the distance from centre...care to explain?
     
  5. Jan 19, 2010 #4

    rl.bhat

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    Homework Helper

    You have to integrate [ intg(r^2*dr - r^3*dr/R)] between 0 to R.
    It is equal to [R^3/3 - R^3/4]
     
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