As ,we know that relation between work and displacement is given by :

Work = force × displacement.

work done is defined as scalar product of force and displacement .

W = F.S

W = FScosθ

if displacement is equal to 0 , then work done must be equal to 0 .

That’s not need to true , if S =0 then W=0.

### Explanation:

#### case 1 :

- It is only true in case of conservative force ( Gravitational force , spring force etc.) , as it is path independent forces , it depends only on initial and final position.
- work done along a closed path is 0 .

### case 2 :

- In case of non conservative forces (Frictional force) , as it path dependent forces.
- work done along closed path is not zero

suppose , a body of mass ‘m’ kg is moved from point A to B , then work done by frictional force is W= f s cos(180°) = -fs.

Now , a body of mass ‘m’ kg is moved from point B to A , then work done by frictional force is W= f s cos(180°) = -fs.

Total Work done = -2 f s , which is not zero even initial and final position is same ( displacement is 0).