$A$ uniform chain of mass $M$ and length $L$ is lying on a smooth horizontal table,with half of its length hanging down. The work done in pulling the entire chain up onto the table is

If the potential energy between two molecules is given by $U = -\frac{A}{r^6} + \frac{B}{r^{12}}$,then at equilibrium,the separation between the molecules and the potential energy are:

$A$ smooth chain of length $2 \,m$ is kept on a table such that its length of $60 \,cm$ hangs freely from the edge of the table. The total mass of the chain is $4 \,kg$. The work done in pulling the entire chain on the table is (Take, $g=10 \,m/s^2$) (in $\,J$)

Consider a one-dimensional motion of a particle with total energy $E$. There are four regions $A, B, C$ and $D$ in which the relation between potential energy $V$,kinetic energy $K$,and total energy $E$ is as given below:
Region $A: V > E$
Region $B: V < E$
Region $C: K < E$
Region $D: V > E$
State with reason in each case whether a particle can be found in the given region or not.

$A$ uniform chain of length $L$ and mass $M$ is placed on a smooth table such that one-fourth of its length hangs over the edge. Find the work done to pull the hanging part of the chain onto the table.

$A$ body of mass $2\, kg$ is situated at a height $5\, m$ above the ground. Its potential energy is reported as $70\, J$. The potential energy of a $3\, kg$ body situated at a height $1\, m$ above the ground will be reported as ................ $J$.