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Tunnel through earth

  • Thread starter erisedk
  • Start date
  • #1
374
7

Homework Statement


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)

Homework Equations




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)
 

Answers and Replies

  • #2
374
7
Sorry, got it.
 
  • #3
178
31
It will melt.
 

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