Explain qualitatively that if we create a whole on the earth throughout its volumeand then drop a ball in the hole then what will be its motion?

IF we consider the earth perfectly spherical then it is symmetrical about any of its diametrical axis.

so if we think of the earth divided about the any diametrical axis then it will be divided into two halves infact two symmetrical halves.

Now think about the gravitational field of each of the halves saperately.

At the centre the net force will be zero but as the ball goes ahead by the virtue of its velocity.The net force force will be towards the 

farther halve (this is so because as we go deeper inside the earth the value of "g" decreases and hence the force) .So the next external force will

be towards the opposite side of the motion of the  ball and hence the net  force will also be opposite to the displacement covered  which is a

satisfactory condition for the S.H.M.So the ball will execute the simple harmpnic motion .