Question

Assuming the earth to be of uniform density, drill a hole through the earth between any two points on the surface of the earth. Install a frictionless tube, and evacuate all the air. Show that the motion of a subway car placed in this tube is simple harmonic motion and evaluate the period of this motion. Note: You must show that your solution is true for a hole between ANY two points on the earth's surface, not just a hold going through the center of the earth. (Hint: Develop a gravitational equivalent of Gauss's Law.)

2) Assuming the earth to be of uniform density, drill a hole through the earth between any two points on the surface of the earth. Install a frictionless tube, and evacuate all the air. Show that the motion of a subway car placed in this tube is simple harmonic motion and evaluate the period of this motion. Note: You must show that your solution is true for a hole between ANY two points on the earths surface, not just a hole going through the center of the earth. (Hint: Develop a gravitational equivalent of Gausss Law

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