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 a constant. The total energy of the particle is -

Options

A. `(K)/(2r)`
B. `-(K)/(2r)`
C. `-(K)/(r )`
D. `(K)/(r )`

Answer

B

Explanation

Here `(m v^(2))/(r) = (K)/(r^(2)) therefore K.E. = (1)/(2) m v^(2) = (K)/(2r)`
`U = -int_(oo)^(r) F.dr = -int_(oo)^(r)(-(K)/(r^(2)))dr = -(K)/(r)`
Total energy `E = K.E. + P.E. = (K)/(2r) - (K)/(r) = -(K)/(2r)`