Suppose a hole is drilled through the center of the Earth and a bowling ball of mass m is dropped into the hole, as shown in the following figure. Construct a mathematical model that describes the motion of the ball. At time t let r denote the distance from the center of the Earth to the mass m, M denote the mass of the Earth, M_rdenote the mass of that portion of the Earth within a sphere of radius r, and δ denote the constant density of the Earth.

Hole through

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surface