$A$ 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.

State the principle of conservation of mechanical energy in the presence of non-conservative forces.

The points of maximum and minimum attraction in the curve between potential energy $(U)$ and distance $(r)$ of a diatomic molecule are respectively:

The potential energy $U(x)$ of a particle is shown in the figure. Which of the following graphs represents the force $F(x)$ acting on it?

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

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: