A straight tunnel is dug through Earth, as shown in Figure
Chapter , Problem 104(choose chapter or problem)
A straight tunnel is dug through Earth, as shown in Figure 14-38. Assume that the walls of the tunnel are frictionless. (a) The gravitational force exerted by Earth on a particle of mass at a distance from the center of Earth when is where is the mass of Earth and is its radius. Show that the net force on a particle of mass at a distance from the middle of the tunnel is given by and that the motion of the particle is therefore simple harmonic motion. (b) Show that the period of the motion is independent of the length of the tunnel and is given by (c) Find its numerical value in minutes.
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