Inside the earth, the surrounding mass exerts a gravitational pull in all directions. Of course, there is more mass towards the center of the earth than any other direction. The magnitude of this force is proportional to the distance from the center. (Can you prove this?) Suppose a hole is drilled to the center of the earth and a mass is dropped in the hole. Ignoring air resistance, with what velocity will the mass strike the center of the earth? As a hint, let x represent the distance of the mass from the center of the earth and note that equation implies that the acceleration is a = v(dv/dx).
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