A spring has been attached to an object which is kept on the ground. The spring is initially in its natural length: 'l' when a force 'F' is applied on it. The force 'F' slowly pulls the object so it does not attain any acceleration. There's a point 'P' on the line which is positioned l/5 units away from the top of the spring when it was in its natural length. After a few moments, the point 'P' is at the same point where the end of the spring earlier was. We are required to determine the work done by the force. There's no air resistance.
I have also attached an image of the diagram.
I aim at solving this question via the Work-Energy Theorem for a system of particles.
The Attempt at a Solution
We haven't been given the value for the constant of spring force, so to determine that, I thought about the elongation of the spring, I thought that elongation should be equal to l/5 but my teacher said I was wrong. What is wrong about the elongation that I calculated? I then thought that since when we pull a spring, each portion of the spring gets elongated equally, if the spring gets elongated by 'x', then the elongation at each portion will have to be x/l, but i don't know if I am right or wrong.