Suppose a smooth tunnel is dug along a s...

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 the earth is uniformly distributed over its volume. Then, which of the following statements are not correct?

the particle will emerge from the other end will velocity `sqrt((GM_(e))/(2R_(e)))`, where `M_(e) and R_(e)` are earth's mass and radius respectively

the overlapping will come to rest at centre of the tunnel

potential energy of the particle will be equal to zero at centre of tunnel if it is along a diameter

acceleration of the particle will be proportional to its distance from mid-point of the tunnel

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