$A$ 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 $g=10 \,m/s^2$)

$A$ particle is constrained to move along the $x$-axis. $A$ force is applied to it in the same direction,which varies with the distance $x$ from the origin as $F(x) = -kx + ax^3$,where $k$ and $a$ are positive constants. What will be the graph of the potential energy $U(x)$ of the particle for $x \ge 0$?

$A$ chain of mass $M$ and length $L$ is placed on a table such that $L/4$ of its length hangs over the edge. What is the work done by an external force to pull the hanging part back onto the table?

$A$ 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).

The potential energy of a body is given by $U = A - Bx^2$ (where $x$ is the displacement). The magnitude of the force acting on the particle is:

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