Assume there is a hole made through the center of the Earth and a ball of mass m is dropped into the hole, see figure below. Create a mathematical model that describes the motion of the ball. Define and use if necessary the gravitational force on the mass m. Hint: At time t assume r is the distance from the center of the Earth to the mass m, M=478R³/3 is the mass of the Earth; M₁-47dr³/3 is the mass of that portion of the Earth within a sphere of radius r, and defines the constant density of the Earth. surface R The figure shows the hole through Earth.

Assume there is a hole made through the center of the Earth and a ball of mass m is dropped into the hole, see figure below. Create a mathematical model that describes the motion of the ball. Define and use if necessary the gravitational force on the mass m. Hint: At time t assume r is the distance from the center of the Earth to the mass m, M=478R³/3 is the mass of the Earth; M₁-47dr³/3 is the mass of that portion of the Earth within a sphere of radius r, and defines the constant density of the Earth. surface R The figure shows the hole through Earth.