Q. A particle of mass $10\, g$ is kept on the surface of a uniform sphere of mass $100\, kg$ and radius $10 \,cm$. Find the work to be done against the gravitational force between them, to take the particle far away from the sphere (you may take $G = 6.67 \times 10^{-11}\, Nm^{2} kg^{-2}$
Gravitation
Solution:
$U_i = -\frac{GMm}{r}$
$U_i = -\frac{6.67 \times 10^{-11} \times 100 \times 10^{-2}}{0.1}$
$U_i = \frac{6.67 \times 10^{-11}}{0.1}$
$= - 6.67 \times 10^{-10}\, J $
We know
$\therefore W = \Delta U $
$= U_f - U_i (\because U_f = 0)$
$\therefore W = - U_i = 6.67 \times 10^{-10}\, J$
