In a gravitational field,if the work done along paths $1, 2$ and $3$ is ${W_1}, {W_2}$ and ${W_3}$ respectively,then:

Write a few remarks on conservative forces.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: In a central force field,the work done is independent of the path chosen.
Reason $R$: Every force encountered in mechanics does not have an associated potential energy.
In the light of the above statements,choose the most appropriate answer from the options given below:

Prove $F = - \frac{dV}{dx}$ for a conservative force.

Is the spring force a conservative or a non-conservative force?

$A$ body falls towards the Earth in air. Will its total mechanical energy be conserved during the fall? Justify.