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Here is the first part of the question:

If there is an object of mass

Do I integrate g(r) = -GMr/R^3 with respect to 'r' to get the change in gravity from the center of the Earth to the surface and then solve from R-0. If so I get a solution of -GM/2R, and that doesn't look at all right to me.

The second half of the question relates back to the first part and asks if mass

If there is an object of mass

*m*at the center of the earth, how much work does it take bring that object up a shaft to the surface? Edit: Earth is uniform density.Do I integrate g(r) = -GMr/R^3 with respect to 'r' to get the change in gravity from the center of the Earth to the surface and then solve from R-0. If so I get a solution of -GM/2R, and that doesn't look at all right to me.

The second half of the question relates back to the first part and asks if mass

*m*is dropped from the surface down a mineshaft to the center of the earth, what will its speed be when it reaches the center. Again, since gravity is changing with respect to the radius, how do I get a solid answer?
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