question_answer

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?                                                                           [JEE MAIN 2013]

A)  \[\frac{5GmM}{6R}\]   

B)       \[\frac{2GmM}{3R}\]

C)  \[\frac{GmM}{2R}\]     

D)       \[\frac{GmM}{3R}\]

Correct Answer: A

Solution :

[a] The kinetic energy at altitude

The gravitational potential energy at altitude

Total energy

Potential energy at the surface is

Req. kinetic energy