$A$ uniform chain of length $L$ and mass $M$ is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If $g$ is the acceleration due to gravity,the work required to pull the hanging part onto the table is:

If the potential energy of a particle of mass $0.1 \ kg$ moving along $x$-axis is $U(x) = 5x(x-4) \ J$,then the speed of the particle is maximum at a position of

$A$ body of weight $1 \, N$ has a potential energy of $1 \, J$ relative to the ground. At what height (in $m$) is it located?

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6}$,where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U(x = \infty) - U_{\text{at equilibrium}}]$,then $D$ is:

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

The work done in pumping out water from a cubical vessel of height $1 \ m$ is approximately ........ $J$ (Take $g = 10 \ m/s^2$ and density of water $\rho = 1000 \ kg/m^3$).