In the rough approximation that the density of the Earth is uniform throughout its interior, the gravitational field strength (force per unit mass) inside the Earth at a distance r from the center is...

In the rough approximation that the density of the Earth is uniform throughout its interior, the gravitational field strength

(force per unit mass) inside the Earth at a distance r from the center is gr/R, where R is the radius of the Earth. (In actual

fact, the outer layers of rock have lower density than the inner core of molten iron.) Using the uniform-density

approximation, calculate the amount of energy required to move a mass m from the center of the Earth to the surface.

Compare with the amount of energy required to move the mass from the surface of the Earth to a great distance away.