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 `|F|=(mv^(2))/(r )`]
`KE=(1)/(2)mv^(2)=(K)/(2r) " "` …..(1)
Now as `F=-(dU//dr), therefore U=- int_(oo)^(r )Fdr = - int_(prop)^(r )-(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)`