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(D) The angular momentum $L$ of a particle moving in a circular orbit is given by $L = mvr$,where $m$ is the mass,$v$ is the orbital velocity,and $r$

Vedclass · Accepted Answer

$\sqrt{R}$

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(D) The angular momentum $L$ of a particle moving in a circular orbit is given by $L = mvr$,where $m$ is the mass,$v$ is the orbital velocity,and $r$ is the radius.For a planet revolving around the sun,the gravitational force provides the necessary centripetal force:$\frac{GMm}{R^2} = \frac{mv^2}{R}$Solving for $v$,we get $v = \sqrt{\frac{GM}{R}}$.Substituting this into the angular momentum formula:$L = m 	imes \sqrt{\frac{GM}{R}} 	imes R$$L = m \sqrt{GM} 	imes \sqrt{R}$Since $m$,$G$,and $M$ are constants,we find that $L \propto \sqrt{R}$.Therefore,the correct option is $D$.

Earth revolves around the sun in a circular orbit of radius $R$. The angular momentum of the revolving Earth is directly proportional to:

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