Q 11-07-186JEE MainJEE Main 2019 (11 Jan, Shift 1)Easy
A satellite is revolving in a circular orbit at a height $h$ from the earth's surface, such that $h \ll R$ where $R$ is the radius of the earth. Assuming that the effect of earth's atmosphere can be neglected, the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is
Answer: (D) $\sqrt{gR}\,(\sqrt{2} - 1)$
Since $h \ll R$, the orbital speed is $v_o = \sqrt{gR}$ and the escape speed from that height is $v_e = \sqrt{2gR}$.
$$\Delta v = \sqrt{2gR} - \sqrt{gR} = \sqrt{gR}\,(\sqrt2 - 1)$$
Solution by Sreeraj P, M.Sc Physics