A particle of mass $$m$$ is moving in a circle of radius $$r$$ under a centripetal force equal to $$ \dfrac{-K}{r^2} \hat{r} $$ where $$K$$ is constant. What is the total energy of the particle ?
Centripetal Area $$ = \dfrac{-K}{r^2} $$
$$ \dfrac{mv^2}{r} = \dfrac{K}{r^2} $$
$$ mv^{2} = \dfrac{K}{r} $$
Kinetic energy $$ = \dfrac{mv^2}{2} = \dfrac{K}{2r} $$
Potential energy at a distance $$r$$ is given as $$ U = \dfrac{-K}{r} $$
So total energy $$ = U + K $$
$$ = \dfrac{-K}{2R} $$