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**Hint**Conservative force has a property that work done in moving a particle between two points is independent of the path taken.

**Complete step-by-step solution**:The work done by such forces

Does not depend upon path.

Depends only and only initial and final position.

For example:- If A and B are the two points and a conservative force acts on point A and B. Then we assume the three ways to go at point B . 1,2 and 3 are the three ways.

If the force is conservative, then work done by this force by first path, by second path and third path are equal.

Let \[{{W}_{1}}\] be the work done along path 1, ${{W}_{2}}$ be the work done along path 2 and ${{W}_{3}}$ be the work done along path 3

Then,

${{W}_{1}}={{W}_{2}}={{W}_{3}}$

Examples of conservative forces are gravitational force , spring force, and electrostatic force.

First we talk about gravitational force, let us assume $\left( m \right)$ .Which is placed on an inclined plane.

For path 1:-

Angle between force $\left( mg \right)$ and displacement $\left( l \right)$ is$\left({{90}^{\circ }}+\theta \right)$

Than $\begin{align}

& {{W}_{1}}=FS\cos \phi \\

& {{W}_{1}}=mgl\left( \cos \left( {{90}^{\circ }}+\theta \right) \right) \\

& \\

\end{align}$ $\left[ \cos \left( {{90}^{\circ }}+\theta \right)=-\sin \theta \right]$

${{W}_{1}}=-mgl\sin \theta $ …………………..(i)

For path 2

First we go from point A to point B and then from point B to point C.

$W={{W}_{AB}}+{{W}_{BC}}$

When we go from A to B then the angle between force and displacement is ${{90}^{\circ }}$ $\left( \cos {{90}^{\circ }}=0 \right)$ .

Than $\begin{align}

& {{W}_{AB}}=FS\cos {{90}^{\circ }} \\

& {{W}_{AB}}=0 \\

\end{align}$

When we go from point B to C then the angle between force and displacement is ${{180}^{{}^\circ }}$.

${{W}_{BC}}=-mgl\sin \theta $

${{W}_{2}}={{W}_{AB}}+{{W}_{BC}}$

${{W}_{2}}=-mgl\sin \theta $ ……………….. (ii)

${{W}_{1}}={{W}_{2}}$

So the work done in the first path is equal to work done in the second path. So it is independent of path.

**Note:**

Students think that whose path has long distance then work done is maximum for that path, but for conservative force work done does not depend on path distance.

Students think that whose path has long distance then work done is maximum for that path, but for conservative force work done does not depend on path distance.

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