A hypothetical straight tunnel is dug from Durban, through the center of the earth, till it comes out from the Island of Hana in Hawaii. A ball of mass 1 kg is dropped in this tunnel from the ground level in Durban. (a) Using the definition of Simple Harmonic Motion, and expression for gravitational force inside the Earth, PROVE that the motion exe- cuted by the ball will be Simple Harmonic about the centre of the earth. (b) What is the amplitude and time period for this Simple Harmonic Motion?
(c) What is the potential energy and the kinetic energy of the ball when it is at a distance "r" from the centre of the earth.