Question

If $V_e$ is the escape velocity and $V_0$ is the orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

• A. $V_0=\sqrt{2}{V}_e$
• B. $V_0=V_e$
• C. $V_e=\sqrt{2V_0}$
• D. $V_e=\sqrt{2}{V}_0$

Answer 1

The correct option is D $V_e=\sqrt{2}{V}_0$

As we know that the escape velocity near the surface of earth is given by

$V_e=\sqrt{\frac{2GM}{R}}$

Similarly, orbital velocity near the surface of the earth will be

$V_o=\sqrt{\frac{GM}{R}}$

$\therefore V_e=\sqrt{2}{V}_0$

$\begin{array}{c}\text{Why this question : To make students}\\ \text{understand the relationship between}\\ \text{escape velocity and orbital velocity.}\end{array}$