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. Prove that the acceleration of the particle will be proportional to its distance from midpoint of the tunnel.
I have tried to find velocity using energy conservation and then differentiate to get acceleration.But I am not getting it right.
Any help is appreciated.
