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  4. A particle of mass m moves in a circular orbit under the central potential field, U ( r )=(- C / r ), where C is a positive constant. The correct radius - velocity graph of the particle's motion is :

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Q. A particle of mass $m$ moves in a circular orbit under the central potential field, $U ( r )=\frac{- C }{ r }$, where $C$ is a positive constant.
The correct radius - velocity graph of the particle's motion is :

JEE MainJEE Main 2021Work, Energy and Power

Solution:

$U =-\frac{ C }{ r }$
$F =-\frac{ d U }{ dr }=-\frac{ C }{ r ^{2}}$
$| F |=\frac{ mv ^{2}}{ r }$
$\frac{ C }{ r ^{2}}=\frac{ mv ^{2}}{ r }$
$v ^{2} \propto \frac{1}{ r }$