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,

the particle will emerge from the other end with velocity $\sqrt{\frac{G{M}_e}{2R_e}}$, 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.