The orbital velocity of a body near the surface of a planet ' A ' is equal to escape velocity of a body from the planet ' B '. If the masses of planets A and B are same, the ratio of their radii is

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$\frac{1}{2}$

$\frac{1}{3}$

answer is B.

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Detailed Solution

The orbital velocity for the planet A is given by $v_{o} = \sqrt{\frac{G M_{A}}{R_{A}}}$

the escape velocity from the surface of B is given by $v_{e} = \sqrt{\frac{2 G M_{B}}{R_{B}}}$

These two velocities are equal, $\frac{M_{A}}{R_{A}} = \frac{2 M_{B}}{R_{B}} \Rightarrow \frac{R_{A}}{R_{B}} = \frac{1}{2}$

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