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Calculating the gravitational field due to a horizontal uniform thin disk

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that the gravitational field due to a horizontal uniform thin disc (thickness D, radius R and density r) at a distance h vertically above the centre of the disc has magnitude

    2πGρd(1-h/(R2+h2)1/2)

    A pendulum clock in the centre of a large room is observed to keep correct time. How many
    seconds per year will the clock gain if the floor is covered by a 1cm thick layer of lead of density
    11350kgm−3?
    [Newton’s gravitational constant is G = 6.67×10−11Nm2 kg−2.]


    2. Relevant equations
    Gravitational potential, [itex]\phi[/itex]=-Gdm/R
    Where dm=2πRDρ.dR
    Gravitational field, g= -[itex]\nabla[/itex][itex]\phi[/itex]

    3. The attempt at a solution
    I have got to [itex]\phi[/itex]=-2πDρGdR and I know I need to integrate with respect to R, then use the g= -[itex]\nabla[/itex][itex]\phi[/itex] but I am unsure what my integration limits should be? I think I need to integrate between 0 and R but then I can't see how I would get the h/(R2+h2)1/2 term?
    Any hints would be very useful.
     
  2. jcsd
  3. Mar 6, 2012 #2
    In the relevant equations sections ϕ=-Gdm/R should be dϕ=-Gdm/R
     
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