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 2R?

Options

A. `(GMm)/(2R)`
B. `(2GMm)/(2)`
C. `(GMm)/(3R)`
D. `(5 GMm)/(2)`

Answer

B

Explanation

The minimum energy required to launch a satellite form surface of earth is equal to the amount of work done against gravity to move it form the surface of earth to a height h and is given by `U = W = GMm ((1)/(r_(1))-(1)/(r_(2)))`
` = GMm ((1)/(R) - (1)/(R +h))`
Here h = 2R
`rArr " " U = GMm ((1)/(R) -(1)/(3R)) = (2GMm)/(3R)`