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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
A
$v_e = \sqrt2v_o$
B
$v_o = \sqrt2v_e$
C
$v_o = v_e$
D
$v_e = \sqrt{2v_o}$
Detailed Solution
Escape velocity: $v_e = \sqrt{\frac{2GM}{R}}$
Orbital velocity close to the surface: $v_o = \sqrt{\frac{GM}{R}}$
$\frac{v_e}{v_o} = \sqrt2 \Rightarrow v_e = \sqrt2v_o$
Orbital velocity close to the surface: $v_o = \sqrt{\frac{GM}{R}}$
$\frac{v_e}{v_o} = \sqrt2 \Rightarrow v_e = \sqrt2v_o$