A particle of mass $m $ is moving in a horizontal circle of radius $r$ under a centripetal force equal to $ - K/{r^2}$, where $K$ is a constant. The total energy of the particle is
A particle of mass $m $ is moving in a horizontal circle of radius $r$ under a centripetal force equal to $ - K/{r^2}$, where $K$ is a constant. The total energy of the particle is
$\frac{K}{{2r}}$
$ - \frac{K}{{2r}}$
$ - \frac{K}{r}$
$\frac{K}{r}$
A particle of mass $m $ is moving in a horizontal circle of radius $r$ under a centripetal force equal to $ - K/{r^2}$, where $K$ is a constant. The total energy of the particle is
Here $\frac{{m{v^2}}}{r} = \frac{K}{{{r^2}}}$
K.E.$ = \frac{1}{2}m{v^2} = \frac{K}{{2r}}$
$U = - \int_\infty ^r {F.dr} = - \int_\infty ^r {\left( { - \frac{K}{{{r^2}}}} \right)} \,dr = - \frac{K}{r}$
Total energy $E = {\rm{K}}{\rm{.E}}{\rm{.}} + {\rm{P}}{\rm{.E}}{\rm{.}} = \frac{K}{{2r}} - \frac{K}{r} = - \frac{K}{{2r}}$
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