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

Define conservative forces. What are the properties of conservative forces?

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:

Give three definitions of conservative force.

The potential energy for a force field $\vec{F}$ is given by $U(x,y) = \cos(x + y)$. The force acting on a particle at the position given by coordinates $(0, \frac{\pi}{4})$ is

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?