$A$ body at rest may have

The variation of potential energy $U$ of a body moving along the $x$-axis with its position $(x)$ is shown in the figure. The body is in an equilibrium state at:

The potential energy between two atoms is given by the function $U(r) = a/r^{12} - b/r^{6}$. Find the equilibrium distance between them.

The potential energy of a particle in a force field is $U(r) = \frac{A}{r^2} - \frac{B}{r}$,where $A$ and $B$ are positive constants and $r$ is the distance of the particle from the centre of the field. For stable equilibrium,the distance of the particle is:

$A$ particle is released from rest at the point $x = a$ and moves along the $x$ axis subject to the potential energy function $U(x)$ shown. The particle:

Write the equation of total mechanical energy of a body having mass $m$ and stationary at height $H$.