Question

Prove that work done in moving a body in a gravitational field is independent of the path followed​

Answer 1

Answer:

Because gravitational field is a conservative field.

Explanation:

The graviational field is considerd as a conservative field. In a conservative field the conservative forces are independent of their path followed. They are dependent only on their initial and final positons. So gravitational force depends only on the height of the object from the ground level. The horizontal displacement made by the object are not considered here.

We have the equation of work done,

        W = F · ds

Where F is the force and ds is the displacement made.

The line integral of the above equatiojn will be

        $W = \int\limits^a_b {F} \, ds$

The line integral depends only on the initial point 'a' and the final point 'b' of the object. so the gravitational force is independent of the path followed.