Q116 / 150 · MHT CET 2019 (Shift 2) · Physics

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 attitude 2R?

A
$\frac{G M m}{2 R}$
Correct answer
B
$\frac{2 G M m}{3 R}$
C
$\frac{G M m}{3 R}$
D
$\frac{5 G M m}{6 R}$

Solution

The minimum energy required to launch a satellite 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 = G M m (\frac{1}{r_{1}} - \frac{1}{r_{2}})

= G M m (\frac{1}{R} - \frac{1}{R + h})

Here, h = 2R

\Rightarrow U = G M m (\frac{1}{R} - \frac{1}{3 R}) = \frac{2 G M m}{3 R}

Hence, the correct answer is option: 'B'.

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