Gravitation 3 Question 3
6. What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ ?
(2013 Main)
(a) $\frac{5 G m M}{6 R}$
(b) $\frac{2 G m M}{3 R}$
(c) $\frac{G m M}{2 R}$
(d) $\frac{G m M}{3 R}$
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Answer:
Correct Answer: 6. (a)
Solution:
- $E$ = Energy of satellite - energy of mass on the surface of planet
$$ =-\frac{G M m}{2 r}–\frac{G M m}{R} $$
Here, $r=R+2 R=3 R$
Substituting in about equation we get, $E=\frac{5 G M m}{6 R}$
