The value of acceleration due to gravity at the centre of earth is zero and at the surface is maximum. When a hole or tunnel is dug along any diameter, the diameter will act as the path of motion. The two ends of the diameter will have maximum acceleration and the middle will have zero acceleration. So, the object dropped into this hole will start to oscillate in such a way that the acceleration will be proportional to the displacement from the mean position and directed towards the mean position. Hence, the object will perform simple harmonic motion.
Home Gravitation Reasonings Suppose a hole is dug along a diameter of the earth. An object is dropped into this hole. Does the object come out from another end?