Q 11-07-017JEE MainEAMCET 2010 (Engineering)Medium
A launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7R$, the minimum energy required to be spent by the launching vehicle on the satellite is
Answer: (B) $\dfrac{13GMm}{14R}$
On the surface (at rest): $E_1 = -\dfrac{GMm}{R}$. In orbit of radius $7R$: $E_2 = -\dfrac{GMm}{2(7R)} = -\dfrac{GMm}{14R}$.
$$E_{min} = E_2 - E_1 = \frac{GMm}{R} - \frac{GMm}{14R} = \frac{13GMm}{14R}$$
Solution by Sreeraj P, M.Sc Physics