See Giancoli-SE: 6-1.
A very wealthy individual proposes to dig a hole through the center of the Earth and
run a train (the small black circle) from one side of the Earth to the other as shown in
the animation (position is in Earth radii and time is in seconds). Which of the animations
correctly depicts the motion of the train? Ignore frictional effects and assume the Earth
is a uniform mass distribution.
The force is related to the total mass beneath the small black mass. See Giancoli-SE: 6-1.
Physlet problem written by Mario Belloni, modified slightly by Evelyn Patterson.