$A$ body at rest may have

$A$ particle is constrained to move along the $x$-axis. $A$ force is applied to it in the same direction,which varies with the distance $x$ from the origin as $F(x) = -kx + ax^3$,where $k$ and $a$ are positive constants. What will be the graph of the potential energy $U(x)$ of the particle for $x \ge 0$?

$A$ uniform chain has a mass $m$ and length $l$. It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done in just pulling the hanging part back on the table is:

$A$ particle moving along the $X$-axis has potential energy $U = 2 - 20x + 5x^2 \text{ J}$. The particle is released at $x = -3 \text{ m}$. What is the maximum value of $x$ reached by the particle (in $\text{ m}$)? ($x$ is in meters and $U$ is in joules)

The potential energy of a particle in a central field has the form $U(r) = \frac{1}{r^2} - \frac{1}{r}$, where '$r$' is the distance from the centre of the field. The magnitude of the maximum attractive force in Newton is

Potential energy is a......