Assume a hole is drilled through the center of the Earth. It can be shown that an object of the 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 k = (4/3) πρGm, where G is the gravitational constant.
