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:

  1. $E$ = 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, $E=\frac{5 G M m}{6 R}$



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