If $v_e$ is escape velocity and $v_o$ is orbital velocity of a satellite for orbit close to the Earth's…

If $v_e$ is escape velocity and $v_o$ is orbital velocity of a satellite for orbit close to the Earth's surface, then these are related by
  1. $v_o=\sqrt{2} v_e$
  2. $v_o=v_e$
  3. $v_e=\sqrt{2 v_o}$
  4. $v_e=\sqrt{2} v_o$

Solution

Orbital velocity of satellite $v_o=\sqrt{\frac{G M}{R}}$...(i) and escape velocity of satellite $v_e=\sqrt{\frac{2 G M}{R}}$...(ii) Hence, $\quad v_e=\sqrt{2} v_o$

Asked in: NEET 2012 (Mains)

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