Q 11-07-210JEE MainMedium
A satellite of mass $m$ is in a circular orbit of radius $2R$ around the earth, where $R$ is the radius of the earth and $g$ the acceleration due to gravity at its surface. The minimum energy required to shift it to a circular orbit of radius $3R$ is
Answer: (D) $\dfrac{mgR}{12}$
Concept. The total energy of a satellite in a circular orbit of radius $r$ is $E = -\dfrac{GMm}{2r}$. The energy to be supplied is the increase in $E$. Use $GM = gR^2$.
Step 1. Energies.
$$E_1 = -\frac{GMm}{4R},\qquad E_2 = -\frac{GMm}{6R}$$
Step 2. Difference.
$$\Delta E = GMm\left(\frac{1}{4R} - \frac{1}{6R}\right) = \frac{GMm}{12R} = \frac{mgR}{12}$$
Answer. $\dfrac{mgR}{12}$ (Option D).
Solution by Sreeraj P, M.Sc Physics