Question

If $v_e$ is escape velocity and $v _o$ is orbital velocity of a satellite for orbit close to the earth's suface, then these are related by

• A. $v_o = \sqrt 2v_e$
• B. $v_o = v_e$
• C. $v_e = \sqrt 2v_o$
• D. $v_e = \sqrt 2$

Answer 1

The Correct Option is C

Escape velocity, $v_e = \sqrt \frac {2GM}{R} \, \, \, \, \, \, ...(i)$
where M and R be the mass and radius of the earth respectively.
The orbital velocity of a satellite close to the earth's surface is
$v_o = \sqrt \frac {GM}{R} \, \, \, \, \, \, \, \, \, \, ...(ii)$
From (i) and (ii), we get
$v_e = \sqrt {2v_o}$