$A$ metal chain of mass $2 \,kg$ and length $90 \,cm$ hangs over a table with $60 \,cm$ on the table. How much work needs to be done to pull the hanging part of the chain back onto the table (in $\,J$)? (Let $g=10 \,m/s^2$)

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

Calculate the work done in rotating a vertical meter scale of mass $400 \, g$ by an angle of ${60^o}$. (in $, J$)

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 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:

$A$ chain of length $L$ and mass $M$ is placed on a frictionless table with one-fifth of its length hanging over the edge. What is the work required to pull the hanging part back onto the table?