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 potential energy graph of a particle is given. Find the corresponding force graph.

For a system of conservative forces,the potential energy $U$ is given by the formula $U = ax^2 - bx$,where $a$ and $b$ are constants. Determine the force $F$.

The work done by the force $\vec{F} = x^2 \hat{i} + y^2 \hat{j}$ around the closed path $OABC$ shown in the figure is:

$A$ particle of mass $m$ with initial kinetic energy $K$ approaches the origin from $x = +\infty$. Assume that a conservative force acts on it and its potential energy $V(x)$ is given by $V(x) = \frac{K}{\exp(3x/x_0) + \exp(-3x/x_0)}$, where $x_0 = 1 \ m$. The speed of the particle at $x = 0$ is

Why are gravitational forces or spring forces considered conservative forces?