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.
Work done in the motion of a body over a closed loop is zero only when the body is moving under the action of conservation forces (like gravitational or electrostatic forces).
A conservative force depends only on the position of the object

It is not zero when the forces are non-conservative e.g. frictional forces

Work done by a conservative force in a closed loop is zero, while work done by a non-conservative force is not necessarily zero for a round trip. This can be explained through the concepts of conservative and non-conservative forces, work, and energy.

Conservative Forces:
- A conservative force is a force whose work done on an object is independent of the path taken and only depends on the initial and final positions of the object.
- Examples of conservative forces include gravitational force, electrostatic force, and spring force.

Non-conservative Forces:
- Non-conservative forces are forces whose work done on an object depends on the path taken.
- Examples of non-conservative forces include friction, air resistance, and tension in a rope.

Work and Energy:
- Work is defined as the transfer of energy from one system to another due to the application of a force over a displacement.
- In physics, work is calculated by multiplying the magnitude of the force applied in the direction of displacement by the distance traveled.
- The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.

Work Done by Conservative Forces:
- When a conservative force acts on an object in a closed loop, such as a complete round trip, the work done by the force is zero.
- This is because, in a closed loop, the object returns to its initial position, and hence, the change in position is zero.
- Since the work done by a conservative force only depends on the initial and final positions, it remains constant along the entire loop, resulting in a net work of zero.

Work Done by Non-conservative Forces:
- Unlike conservative forces, non-conservative forces do not exhibit the property of work being zero in a closed loop.
- The work done by a non-conservative force depends on the path taken by the object and not just its initial and final positions.
- For example, in the case of friction, the work done by friction depends on the distance traveled and the roughness of the surface, leading to a non-zero work even in a closed loop.

Conclusion:
In summary, the work done by a conservative force in a closed loop is zero because it only depends on the initial and final positions of the object. However, the work done by a non-conservative force is not necessarily zero for a round trip as it depends on the path taken by the object. Understanding these concepts helps in analyzing and determining the energy transfers and transformations in different physical systems.