(D) The centripetal force $F$ acting on a particle of mass $m$ moving in a circular path of radius $r$ with velocity $v$ is given by $F = \frac{m v^{2

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(D) The centripetal force $F$ acting on a particle of mass $m$ moving in a circular path of radius $r$ with velocity $v$ is given by $F = \frac{m v^{2}}{r}$.We know that the angular momentum $L$ of a particle is given by $L = mvr$.From this,we can express the velocity as $v = \frac{L}{mr}$.Substituting this expression for $v$ into the centripetal force formula:$F = \frac{m}{r} \left( \frac{L}{mr} \right)^{2} = \frac{m}{r} \cdot \frac{L^{2}}{m^{2} r^{2}} = \frac{L^{2}}{m r^{3}}$.Therefore,the correct option is $D$.

Class 11 Physics 3-2.Motion in Plane Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

Medium

$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is

MHT CET 2009 All MHT CET

A
$\frac{L^{2}}{m r}$
B
$\frac{L^{2} m}{r}$
C
$\frac{L^{2}}{m^{2} r^{2}}$
D
$\frac{L^{2}}{m r^{3}}$

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3-2.Motion in Plane

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Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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$A$ particle of mass $m$ is rotating in a plane in a circular path of radius $r$. Its angular momentum is $L$. The centripetal force acting on the particle is

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