Given below is the plot of a potential energy function $U(x)$ for a system,in which a particle is in one-dimensional motion,while a conservative force $F(x)$ acts on it. Suppose that $E_{\text{mech}} = 8 \, J$,the incorrect statement for this system is:

When a conservative force does positive work on a body,

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:

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.

Which one of the following is not a conservative force?

The potential energy of a certain particle is given by $U = \frac{1}{2}\,(x^2 - z^2)$. The force on it is: