Q 11-07-007NEETNEET 2024Top questionMedium
The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$ from the surface of the earth is:
Answer: (C) $\dfrac{5GmM}{6R}$
Orbit radius: $r = R + 2R = 3R$.
Energy on the surface (at rest): $E_1 = -\dfrac{GMm}{R}$.
Total energy in the orbit: $E_2 = -\dfrac{GMm}{2r} = -\dfrac{GMm}{6R}$.
$$\Delta E = E_2 - E_1 = \frac{GMm}{R} - \frac{GMm}{6R} = \frac{5GMm}{6R}$$
Solution by Sreeraj P, M.Sc Physics