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?

• A. $\frac{3GMm}{5R}$
• B. $\frac{GMm}{2R}$
• C. $\frac{2}{15}\frac{GMm}{R}$
• D. $\frac{GMm}{5R}$

Answer 1

The correct option is C $\frac{2}{15}\frac{GMm}{R}$

Work done is shifting a body from an orbit of radius $3R$ to $5R$ is equal to change in potential energy of the body.

Potential energy $=\frac{-GMm}{r}$

where $M$ is mass of the earth $m$ is mass of satellite $r$ is radius of orbit

$W=$ Final potential energy $-$ Initial potential energy

$W=\frac{-GMm}{5R}-\left(\frac{-GMm}{3R}\right)$

$=\frac{GMm}{R}(\frac{1}{3}-\frac{1}{5})=\frac{2GMm}{15R}$