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A particle of mass m is moving in a hori...

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. The total energy of the particle is

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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).`
`thereforeU=-underset(oo)overset(r)int Fdr=-underset(oo)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)`
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