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?

When the particle is dropped in the tunnel at its one end , it starts to execute simple harmonic motion with mean position as the centre of the tunnel. Hence, acceleration of the particle is directly proportional to its distance from the centre of the tunnel. It means, option (d) is correct.

The particle has zero velocity at one end because it is dropped from rest at that end, therefore, ends of the tunnel are its extreme positions. Hence, at the other end, the velocity will become equal to zero. It means option (a) is incorrect.

Velocity of a particle executing S.H.M. is maximum at its mean position. Hence, at the centre of the tunnel , its velocity will be maximum possible. Hence, option (b) is incorrect.
When the particle moves from extreme position to centre of the tunnel, its velocity increases . It means KE increases or PE decreases . But initial potential energy of the particle is negative . Hence, potential energy be comes more negative and it is least at the mid-point of the tunnel because K E is maximum there. It means the gravitational PE can never be equal to zero. Hence. option (c) is also incorrect