Discussion Forum



1)

What is the minimum energy required to launch a  satellite of mass 'm' from the surface of the earth of mass 'M'  and radius  'R'  at an altitude 2R?


A) $\frac{GMm}{2R}$

B) $\frac{2GMm}{3R}$

C) $\frac{GMm}{3R}$

D) $\frac{5GMm}{6R}$

Answer:

Option B

Explanation:

 The minimum energy required to launch a satelite  from surface of earth  is equal to the amount of work done against gravity to move it from  the surface of earth  to a height h and is given by

$U=W=GMm(\frac{1}{r_{1}}-\frac{1}{r_{2}})$

  $=GMm(\frac{1}{R}-\frac{1}{R+h})$

 Here, h= 2R

$\Rightarrow $    $U=GMm(\frac{1}{R}-\frac{1}{3R})=\frac{2GMm}{3R}$