$A$ body is moved along a closed loop. Is the work done in moving the body necessarily zero? If not,state the condition under which work done over a closed path is always zero.

Conservative forces are defined as the force for which,

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:

Given below are two statements:
Statement $I$: An object moves from position $r_{1}$ to position $r_{2}$ under a conservative force field $\vec{F}$. The work done by the force is $W = -\int_{r_{1}}^{r_{2}} \vec{F} \cdot d\vec{r}$.
Statement $II$: Any object moving from one location to another location can follow an infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of the above statements, choose the correct answer from the options given below:

There will be a decrease in the potential energy of the system if work is done upon the system by:

Assertion $(A) :-$ If work done by the force depends on the path,then the force is said to be non-conservative.
Reason $(R) :-$ All conservative forces are central forces.