Describe the motion of a ball dropped into a theoretical hole drilled from the surface of the Earth, through its core to the other surface.

Make assumptions:No air resistanceEarth is perfectly sphericalEarth is of uniform densitySimple harmonic motion, the ball would oscillate between the position dropped and the corresponding position on the other side of the Earth. Max displacement (from the centre of the Earth) and max acceleration is at the position where the ball is dropped (and the corresponding position), max max speed is at the centre of the Earth.Furthering the question can include; what happens when the ball is thrown down the hole (larger amplitude), consider air resistance (damping of oscillations).Students may have to be guided through some parts of the question, or encouraged to think about simplifying assumptions.