question_answer

A satellite is revolving in a circular orbit at a height h from the earth surface, such that \[h<<R\] where R is the radius of the earth.                                        Assuming that the effect of earths atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is-                         [JEE Main 11-Jan-2019 Morning]

A) \[\sqrt{2gR}\]    

B)      \[\sqrt{gR}(\sqrt{2}-1)\]

C) \[\sqrt{\frac{gR}{2}}\]                D)      \[\sqrt{gR}\] Correct Answer: B Solution : [b] The escape speed of the satellite is

The orbital speed of the satellite at height h is

Hence, the minimum increase in speed so that the satellite could escape is