How orbital and escape velocities are related?

v_{e} = 2 v_{0}

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v_{e} = \sqrt{3} v_{0}

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v_{e} = 1.31 v_{0}

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v_{e} = 1.41 v_{0}

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Solution

The correct option is D $v_{e} = 1.41 v_{0}$
Orbital velocity $v_{o} = (\frac{G M}{R})^{0.5}$
Escape velocity $v_{e} = (\frac{G M}{R})^{0.5}$
Taking ratio, $\frac{v_{e}}{v_{o}} = (\frac{2 G M}{R})^{0.5} \times (\frac{R}{G M})^{0.5}$
So, $v_{e} = 2^{0.5} v_{o} = 1.41 v_{o}$

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