Question:
A particle of mass $100 \mathrm{~g}$ is kept on the surface of a uniform sphere of mass $10 \mathrm{~kg}$ and radius $10 \mathrm{~cm}$. Find the work to be done against the gravitational force between them to take the particle away from the sphere.
Solution:
Work done against gravitational force $=$ change in potential energy
$W=U_{f}-U_{i}$
$W=0-\left(-\frac{G M m}{r}\right)$
$W=\frac{G M m}{r}=\frac{6.67 \times 10^{-11} \times 0.1 \times 10}{0.1}$
$W=6.67 \times 10^{-10} \mathrm{~J}$