Question

what if stone is dropped in a hole from north pole to south pole

Answer 1

They would both head for the center of the earth. But they would collide on the way. The separation when they emerge on the other side would depend on their diameter and elasticity. Larger balls would collide earlier and have more time to separate. If the elasticity is zero, they would stick together and emerge with zero separation. If the collision is perfectly elastic, they would separate at the same velocity that they came together. the problem become more complex because they are no longer move directly toward the center of the earth. If, however the person asking the question finds a way to eliminate the collision, the balls emerge with the same separation as when they entered. Each travels on a line to the center of the Earth. Its momentum brings it up to the surface on the exact opposite side. From there, it reverses direction, falls back through the center and continues to its starting point