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Confusing Question

  1. Mar 20, 2006 #1
    Question: A spehrical planet of Radius R has a density p which depends on the distance r from its centre according to the formula

    [tex]p = \frac{p_0}{1 + (r/R)^2} [/tex]​

    where [tex] p_0 [/tex] is a constant. By dividing the planet up into spherical shells of a small thickness dr, find the mass of the planet.

    Ok so im pretty confused on what im to do here. Do i differentiate with respect to r?
     
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  3. Mar 20, 2006 #2

    0rthodontist

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    You want to find the mass of a spherical shell. Then you want to integrate that mass with r going from 0 to R to find the sum of all the spherical shells that make up the planet.
     
  4. Mar 21, 2006 #3

    HallsofIvy

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    Imagine a shell of radius r, thickness dr. For small dr, its volume is approximately the surface area of the shell, [itex]4\pi r^2[/itex], times the thickness, dr: that is [itex]dV= 4\pi r^2 dr[/itex]. Of course, the mass of that shell is the density at that radius times the volume:
    [tex] 4\pi\frac{p_0 r^2 dr}{1+\left(\frac{r}{R}\right)^2}[/tex]
    Integrate that from 0 to R.
     
  5. Mar 21, 2006 #4
    ok thanks, and that will be the answer because by intergrating i find the sum of all the smaller parts?
     
  6. Mar 21, 2006 #5

    HallsofIvy

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    That's a very rough way of putting it, but okay.
     
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