A particle of mass m is rotating in a plane is a circular path of radius r , its angular momentum is

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6.System of Particles and Rotational Motion

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

A

$\frac{{{L^2}}}{{mr}}$

B

$\frac{{{L^2}m}}{r}$

C

$\frac{{{L^2}}}{{m{r^2}}}$

D

$\frac{{{L^2}}}{{m{r^3}}}$

Solution

$\mathrm{L}=\mathrm{mvr}$

$\therefore \quad \mathrm{v}=\frac{\mathrm{L}}{\mathrm{mr}}$

$\mathrm{F}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\frac{\mathrm{m}\left(\frac{\mathrm{L}}{\mathrm{mr}}\right)^{2}}{\mathrm{r}}$

$\therefore \quad \mathrm{F}=\frac{\mathrm{L}^{2}}{\mathrm{mr}^{3}}$

Standard 11

Physics

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