Question

Show that the workdone in gravitational field is independent of path

Answer 1

The work done by gravity on an object is independent of the path taken because gravity is a conservative force.

The gravitational force is a conservative force because it can be derived from a potential energy function, which means the work done by gravity only depends on the initial and final positions of the object, not on the specific path taken.

Mathematically, the work done
`(\(W\))` by gravity is given by:

`\[ W = -\Delta U \]`

where
`\(U\)` is the gravitational potential energy. The negative sign indicates that work is done against gravity when an object moves upward.

Since the gravitational force is conservative, the change in gravitational potential energy
`(\(\Delta U\))` is the same for any path between two points.

Therefore, the work done by gravity is independent of the path taken. This principle is a consequence of the conservative nature of gravitational forces and is known as the conservative property of gravity.