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College Physics Question: How much energy does it take to completely tear the earth apart? The result only contains g, m, r, urgent,
The gravitational potential energy between a sphere with radius r and a spherical shell with thickness dr is

-g*m^2/(4/3 π*r^3)^2 * 4/3 π*r^3 * 4 π*r^2*dr/r

= - 3 G*M^2 / R^6 * r^4*dr

3gm 2/(5r) for integration