Assume a hole is drilled through the center of Earth. It can shown that an object of mass m at a distance r from the center of Earth is pulled toward the center only by material in the shaded portion of the figure. Assume Earth has a uniform density ρ. a) Starting from Newton's law of universal gravitation, show that the force on m is in the form of Hooke's law. b) What is the spring constant k equal to in this case?

Assume a hole is drilled through the center of Earth. It can shown that an object of mass m at a distance r from the center of Earth is pulled toward the center only by material in the shaded portion of the figure. Assume Earth has a uniform density ρ. a) Starting from Newton's law of universal gravitation, show that the force on m is in the form of Hooke's law. b) What is the spring constant k equal to in this case?

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