Work done by a conservative force on an object at a closed path is
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conservative force is a force with the property that the total work done in moving a particle between two points is independent of the taken path.[1] Equivalently, if a particle travels in a closed loop, the total work done (the sum of the force acting along the path multiplied by the displacement) by a conservative force is zero.[2]
A conservative force depends only on the position of the object.
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The total work done is the product of force acting on the object and the displacement. As, the displacement is zero, the work done will be zero.
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