GravitationHard
Question
Suppose a smooth tunnel is dug along a straight line joining two points on the surface of the Earth and a particle is dropped from rest at its one end. Assume that mass of Earth is uniformly distributed over its volume. Then
Options
A.The particle will emerge from the other end with velocity 
where Me and Re are Earth′s mass and radius respectively
where Me and Re are Earth′s mass and radius respectivelyB.The particle will come to rest at centre of the tunnel because at this position, particle is closest to Earth centre.
C.Potential energy of the particle will be equal to zero at centre of tunnel if it is along tunnel′s diameter
D.Acceleration of the particle will be proportional to its distance from midpoint of the tunnel
Solution
Acceleration of the particle from the centre of the earth is directly proportional to the distance from the centre
⇒ a =
⇒ a ∝ x ⇒ a = ω2x
Particle will perform oscillatory motion.
⇒ a =
⇒ a ∝ x ⇒ a = ω2xParticle will perform oscillatory motion.
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