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Gravitational Force

  1. Mar 22, 2015 #1
    A large spherical planet of radius R made of a material of density d, has a spherical cavity of radius R/2, with center of cavity a distance R/2 from the centre of the planet. Find the gravitational Force on a small mass m at the centre of the cavity
     
  2. jcsd
  3. Mar 22, 2015 #2

    haruspex

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    As per forum rules, you should quote any relevant standard equations of which you are aware and must show some attempt at a solution. If totally stuck, you should at least be able to provide some thoughts.
     
  4. Mar 22, 2015 #3
    using the formula F = Gm1m2/r^2, i am getting 16Gpidrm/3 but the solution is 2Gpidrm/2
     
  5. Mar 22, 2015 #4

    haruspex

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    I get ##\frac 23 G\pi d r m## (I'm guessing the "/2" in what you posted is a typo).
    Please post your working.
    (There is a very quick method here.)
     
  6. Mar 22, 2015 #5
    Yes your answer is right...but how did you do it?
     
  7. Mar 22, 2015 #6
    I used Gm1m2/r^2
    So F = (G(d*4/3pir^3)m)/(r/2)^2
     
  8. Mar 23, 2015 #7

    haruspex

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    That formula is essentially for point masses. It also works if one mass is a uniform spherical shell (or assembly of concentric uniform spherical shells) and the other (point) mass is outside all the shells.
    The trick when dealing with cavities is to treat the cavity as filled in (i.e. no cavity) then add a 'negative mass' at the cavity. so in this case we have a complete sphere (S1 radius R minus a complete sphere (S2) radius R/2.
    What do you know about the gravitational field inside a uniform spherical shell?
    What is the force on m due to S1?
    What is the force on m due to S2?
     
  9. Mar 27, 2015 #8
    Can you show it to me the solved part..?
     
  10. Mar 27, 2015 #9

    haruspex

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