In the equation $W = -mgh$,what does the negative sign indicate?

The following figure shows the variation of potential energy $V(x)$ of a particle with distance $x$. The particle has

For the stability of a physical system,what should be its potential energy? Should it be more or less?

$A$ 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).

Calculate the work done by pump $P$ to transfer water of density $d$ from one container to another as shown in the figure.

Potential energy as a function of $r$ is given by $U = \frac{A}{r^{10}} - \frac{B}{r^{5}}$,where $r$ is the interatomic distance,and $A$ and $B$ are positive constants. The equilibrium distance between the two atoms will be