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 constant. What is the total energy of the particle?

Explanation

As the particle is moving in a circle
`(mv^(2))/(r ) + (K)/(r^(2))` [for circular motion on `|F|= (mv^(2))/(r )`]
KE `=(1)/(2) mv^(2) = (K)/(2r)` ….(1)
Now as `F= -(dU//dr)`
`therefore U= - int_(oo)^(r ) Fdr = - underset(prop)overset(r )int - (k)/(r^(2)).dr`
`U= - (K)/(r )` ....(2)
So Total energy `E= U+ K`
`= - (K)/(r ) + (K)/(2r)` From (1) & (2) i.e., `E= - (K)/(2r)`