First slide

Motion of planets and satellites

Question

In order to shift a body of mass m from a circular orbit of radius 3R to a higher orbit of radius 5R around the earth, the work done is

Moderate

A

$\frac{3 GMm}{5 R}$
B

$\frac{GMm}{2 R}$
C

$\frac{2}{15} \frac{GMm}{R}$
D

$\frac{GMm}{5 R}$

Solution

$\begin{array}{l} W = [- \frac{GMm}{5 R}] - [\frac{GMm}{3 R}] \\ = \frac{GMm}{3 R} - \frac{GMm}{5 R} \\ = \frac{GMm}{R} [\frac{1}{3} - \frac{1}{5}] = \frac{2}{15} \frac{GMm}{R} \end{array}$

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