CBSE Class 11-science Answered

Any force, such as the gravitational force between the Earth and another mass, whose work is determined only by the final displacement of the object acted upon is called conservative force. The total work done by a conservative force is independent of the path resulting in a given displacement and is equal to zero when the path is a closed loop

For a proof of that these are path independent, let's imagine two paths 1 and 2, both going from point A to point B. The variation of energy for the particle, taking path 1 from A to B and then path 2 backwards from B to A, is 0; thus, the work is the same in path 1 and 2, i.e., the work is independent of the path followed,