If a particle of mass $m$ is moving in a horizontal circle of radius $r$ with a centripetal force $( - k/{r^2})$, the total energy is
If a particle of mass $m$ is moving in a horizontal circle of radius $r$ with a centripetal force $( - k/{r^2})$, the total energy is
$ - \frac{k}{{2r}}$
$ - \frac{k}{r}$
$ - \frac{{2k}}{r}$
$ - \frac{{4k}}{r}$
If a particle of mass $m$ is moving in a horizontal circle of radius $r$ with a centripetal force $( - k/{r^2})$, the total energy is
$\frac{{m{v^2}}}{r} = \frac{k}{{{r^2}}}$ $⇒$ $m{v^2} = \frac{k}{r}$
$\therefore K.E.$ = $\frac{1}{2}m{v^2} = \frac{k}{{2r}}$
$P.E. = \int {F\,dr} $ $ = \int {} \frac{k}{{{r^2}}}dr = - \frac{k}{r}$
Total energy $= K.E. + P.E.$ $ = \frac{k}{{2r}} - \frac{k}{r} = - \frac{k}{{2r}}$