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

$A$ rod of length $4 \ m$ and mass $20 \ kg$ is lying horizontally on the ground. Calculate the work done in $J$ to keep it in a vertical position such that one end remains in contact with the ground.

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.

Given in the figures are examples of some potential energy functions in one dimension. The total energy of the particle is indicated by a cross on the ordinate axis. In each case,specify the regions,if any,in which the particle cannot be found for the given energy. Also,indicate the minimum total energy the particle must have in each case. Think of simple physical contexts for which these potential energy shapes are relevant.

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

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