Gravitation

JEE Main level, single correct, medium

187 of 223

Question 187 of 223

A body is moving in a low circular orbit about a planet of mass MM and radius RR. The radius of the orbit can be taken to be RR itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is:

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Answer: (A) 12\dfrac{1}{\sqrt{2}}

The orbital velocity of the body in an orbit of the radius RR is vo=GmR{v}_{o}=\sqrt{\dfrac{Gm}{R}}
The escape velocity from the surface is ve=2GmR{v}_{e}=\sqrt{\dfrac{2Gm}{R}}
Ratio, v0ve=GmR2GmR=12\dfrac{{v}_{0}}{{v}_{e}}=\dfrac{\sqrt{\dfrac{Gm}{R}}}{\sqrt{\dfrac{2Gm}{R}}}=\dfrac{1}{\sqrt{2}}

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