Assume that the earth is a uniform density spherical mass. (This assumption is not correct but we will use it for simplicity in working the problem.) The deepest hole drilled into the earth's surface went to a depth of 40,230 ft (Wikipedia.org). Imagine that this hole was straight toward the center of the earth and that a small 50 kg spherical mass was dropped into the hole and ended up at the very bottom of it. What would be the weight of the spherical mass at that location?
The Attempt at a Solution
This is a two shell theorem problem. Since we all know that w=mg, F=GMm/r2. I think we have to find the gravitational force of the object that is at bottom of the earth and then multiply it by its mass. This will give us the weight of the object.