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  4. A planet with radius R and acceleration due to gravity g, will have atmosphere only if r.m.s. speed of air molecules is less than

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Q. A planet with radius $R$ and acceleration due to gravity $g$, will have atmosphere only if r.m.s. speed of air molecules is less than

KEAMKEAM 2021

Solution:

Minimum speed of air molecules, so that they could escape the planet is given as
$v_e =\sqrt{2 g R} $
$ =1.414 \sqrt{g R}$
So, the planet will have atmosphere only, if rms speed of molecules of air is $1.414 \sqrt{g R}$.