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Question

# Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel. The motion of the particle as seen from the earth is

A

simple harmonic

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B

parabolic

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C

on a straight line

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D

periodic

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Solution

## The correct options are C on a straight line D periodic This should be verified. If the particle is released from height h the force on it when it is out of the tunnel is F=GMem(R+h)2=ma a=GM(R+h)2 you mean, this ain't no SHM equation! but while it comes inside the tunnel, let's say x distance from center M′=MX3R3 Fx=−GMmR3x ax=−GMR3x yeah, that's more like it. So clearly the motion is not SHM The particle reaches Q with velocity v as inside the tunnel its doing SHM. After coming out the particle goes straight up and free falls under gravity taking time 2vg So the total time period is fixed and the path is a straight line, not parabola. Hence options C&D are correct

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