Q 11-07-099JEE MainJEE Main 2023 (11 Apr, Shift 2)Medium
A space ship of mass $2\times10^4\ \text{kg}$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $g=10\ \text{m s}^{-2}$ and radius of earth $=6400\ \text{km}$)
Answer: (B) $8(\sqrt2-1)\ \text{km s}^{-1}$
Orbital speed near the surface $v_o=\sqrt{gR}=\sqrt{10\times6.4\times10^6}=8\ \text{km s}^{-1}$; escape speed $\sqrt2v_o$.
Extra speed $=(\sqrt2-1)\times8\ \text{km s}^{-1}$.
Solution by Sreeraj P, M.Sc Physics