Question

a force acting on a particle is conservative, then

Answer 1

Equivalently, if a particle travels in a closed loop, the net work done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero. Aconservative force is dependent only on the position of the object. ... Thus, all central forces are conservative forces.

Answer 2

A force acting on a particle is conservative then:

1.it obeys Newton's third law or 2.it is not a frictional force or 3. it obeys Newton's second law its work equals the change in the kinetic energy of the particle or 4.its work is zero when the particle moves exactly once around any closed path