Question

The escape velocity for a planet is $v_{e}$. A particle is projected from its surface with a speed $v$. For this particle to move as a satellite around the planet,

• A. $\frac{v_{e}}{2} < v < v_{e}$
• B. $\frac{v_{e}}{\sqrt{2}} < v < v_{e}$
• C. $v_{e} < v < \sqrt{2} v_{e}$
• D. $\frac{v_{e}}{\sqrt{2}} < v < \frac{v_{e}}{2}$

Answer 1

Answer: (B)

For a satellite orbiting very close to the earth's surface, the orbital velocity $=\sqrt{R g}$. This is equal to the velocity of projection and is the minimum velocity required to be in an orbit, if $v >v_{e}$ then the satellite will escape from earth's gravitational pull and will not orbit around the earth
where $v_{e}=\sqrt{2 g R}=\sqrt{2} v$
$ \therefore \frac{v_{e}}{\sqrt{2}} < v < v_{e}$