The diagrams represent the potential energy $U$ as a function of the inter-atomic distance $r$. Which diagram corresponds to stable molecules found in nature?

The potential energy of a particle is related to the $x$ coordinate by the equation $U = x^2 - 2x$. The particle will be in stable equilibrium at:

In the figure shown,the potential energy $(U)$ of a particle is plotted against its position $x$ from the origin. The particle at:

The potential energy of a particle of mass $1 \ kg$ moving freely along the $x$-axis is given by $V(x) = (\frac{x^4}{4} - \frac{x^2}{2}) \ J$. If the total mechanical energy of the particle is $2 \ J$,what is its maximum speed in $m/s$?

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:

$A$ carpet of mass $M$ made of a material is rolled along its length in the form of a cylinder of radius $R$ and kept on a rough floor. If the carpet is unrolled without sliding to a radius $R/2$,the change in potential energy is ($g=$ acceleration due to gravity).