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

JEE MainJEE Main 2020Gravitation

Solution:

$V _{\text {orbit }}=\sqrt{\frac{ GM }{ R }}$
$V _{\text {escape }}=\sqrt{\frac{2 GM }{ R }}$
$\frac{ V _{\text {orbit }}}{ V _{\text {escape }}}=\frac{1}{\sqrt{2}}$