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 $=\sqrt{Rg}$. 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 $v_e=\sqrt{2gR}=\sqrt{2}v$
$\therefore \frac{v_e}{\sqrt{2}}<v<v_e$