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Tunnel through earth

  1. Feb 7, 2015 #1
    1. The problem statement, all variables and given/known data
    A particle is dropped from a height equal to the radius of the earth into a tunnel dug through the earth along one of the diameters. Which of the following is/are true--
    (A) Particle will oscillate through the earth to a height R on both sides
    (B) Particle will execute simple harmonic motion
    (C) Motion of the particle is periodic
    (D) Particle passes through the centre of earth with a speed √ (2GM/R)

    2. Relevant equations


    3. The attempt at a solution
    The answers are (A), (C), (D).

    I know A and C will be true, A due to conservation of energy and C because such motions are almost always periodic, but I don't get why (B) is wrong and (D) is true.
    Is (B) wrong because field above the earth is GM/r^2 and inside the earth GMr/R^3 and these are different, so it won't be SHM?
    In any case, I can't prove (D) to be true (I tried energy conservation)
     
  2. jcsd
  3. Feb 7, 2015 #2
    Sorry, got it.
     
  4. Feb 7, 2015 #3
    It will melt.
     
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