What is the gravitational potential energy of a body of mass $m$ at a distance $r$ from the center of the Earth of mass $M$?

Solution

1. The gravitational potential energy $U$ is defined as the work done to bring a mass from infinity to a distance $r$.
2. The expression for this energy is $U=-{\int }_{\infty }^{r}Fdr$.
3. Substituting $F=\frac{GMm}{r^2}$, we get $U=-\frac{GMm}{r}$.
4. Hence the answer is (B).