The potential energy of a diatomic molecule is given by $U = \frac{A}{{{r^{12}}}} – \frac{B}{{{r^6}}}$ . $A$ and $B$ are positive constants. The distance $r$ between them at equilibrium is 

A block of mass $1\,kg$ is pushed up a surface inclined to horizontal at an angle of $30^o$ by a force of $10\,N$ parallel to the inclined surface (figure). The coefficient of friction between block and the incline is $0.1$. If the block is pushed up by $10\,m$  along the inclined calculate 

$(a)$ work done against gravity

$(b)$ work done against force of friction

$(c)$ increases in potential energy

$(d)$ increases in kinetic energy

$(e)$ work done by applied force

If the potential energy of a gas molecule is $U = \frac{M}{{{r^6}}} – \frac{N}{{{r^{12}}}},M$ and $N$ being positive constants, then the potential energy at equilibrium must be

$A$ & $B$ are blocks of same mass $m$ exactly equivalent to each other. Both are  placed on frictionless surface connected by one spring. Natural length of spring is $L$  and force constant $K$. Initially spring is in natural length. Another equivalent block $C$  of mass $m$ travelling at speed $v$ along line joining $A$ & $B$ collide with $A$. In  ideal condition maximum compression of spring is :-

A sphere of mass $0.1\,\,kg$  is attached to a cord of $1\,m$ length. Starting from the height of its point of suspension this sphere hits a block of same mass at rest on a frictionless table. If the impact is elastic, then the kinetic energy of the block after the collision is …………. $\mathrm{J}$