Assume a hole is drilled through the center of the Earth. It can be shown that an object of mass m at a distance r from the center of the Earth is pulled toward the center only by the material in the shaded portion of Figure P13.73. Assume Earth has a uniform density ρ. Write down Newton’s law of gravitation for an object at a distance r from the center of the Earth and show that the force on it is of the form of Hooke’s law, F = –kr, with an effective force constant of  πρGm, where G is the gravitational constant.FIGURE P13.73

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Chapter1: Units, Trigonometry. And Vectors
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Assume a hole is drilled through the center of the Earth. It can be shown that an object of mass m at a distance r from the center of the Earth is pulled toward the center only by the material in the shaded portion of Figure P13.73. Assume Earth has a uniform density ρ. Write down Newton’s law of gravitation for an object at a distance r from the center of the Earth and show that the force on it is of the form of Hooke’s law, F = –kr, with an effective force constant of  width= πρGm, where G is the gravitational constant.

FIGURE P13.73

 width=

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