If $F = 2x^2 - 3x - 2$,then select the correct statement.

The potential energy of an object is $U(x) = (5x^2 - 4x^3) \ J$,where $x$ is the position in meters. The position at which the force becomes zero is

The variation of force $F$ acting on a body moving along the $x$-axis with respect to its position $(x)$ is shown in the figure. The body is in a stable equilibrium state at:

$A$ 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.

The potential energy of an object of mass $m$ moving in the $xy$ plane in a conservative field is given by $U = ax + by$,where $x$ and $y$ are position coordinates of the object. Find the magnitude of its acceleration.

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: