Question

A space station is set up in space at a distance equal to earth's radius from earth's surface. Suppose a satellite can be launched from space station. Let $V_1$ and $V_2$ be the escape velocites of the satlhte on earth's surface and space station respectively. Then

• A. $V_2=V_1$
• B. $V_2$
• C. $V_2>V_1$
• D. No relation

Answer 1

Answer: (B)

For an object to escape from an orbit, its total energy must be zero. For space station: $T . E =\frac{1}{2} mv _{2}^{2}+\left(-\frac{ GMm }{2 R }\right)=0$ $\Longrightarrow v_{2}=\sqrt{\frac{G M}{R}}$ where $R$ is the radius of earth. For earth's surface : $v_{1}=\sqrt{\frac{2 GM }{ R }}$
Hence $v_{1}>v_{2}$