A particle is moving in a circular path of radius a under the action of an attractive potential U = −k²/r². Its total energy is:

We know, Fx = −dU/dx where →x and →F are in the same direction. Here, radius vector →r and centripetal force →Fr are in opposite directions. Hence Fr = dU/dr
F = dU/dr
F = kr³ = mv²/r
K.E. = 1/2mv² = k²/r²
T.E. = P.E. + K.E. = −k²/r² + k²/r² = 0