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Find velocity of object dropped through hole in center of earth

  1. Feb 12, 2008 #1
    [SOLVED] Find velocity of object dropped through hole in center of earth

    1. The problem statement, all variables and given/known data
    Suppose that a hole has been drilled through the center of the Earth, and that an object is dropped into this hole. Write a first-order differential equation for the object's velocity, v as a function of the distance r from the Earth's center (i.e., an equation involving dv/dr), and solve it to determine the speed the object achieves as it reaches the center of the Earth. Check this speed with the result you get from simple conservation of energy considerations. Consider the Earth's mass density to be uniform throughout. [Hint: recall Gauss' Law as it applies to the gravitational field of a spherically symmetric mass distribution.]
  2. jcsd
  3. Feb 12, 2008 #2


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    Welcome to PF,

    What have you attempted thus far?
  4. Feb 12, 2008 #3
    Solved it thanks
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