A spring of force constant $K$ is first stretched by distance a from its natural length and then further by distance $b$. The work done in stretching the part $b$ is ………….

Two blocks $A$  and  $B$  of masses  $1\,\,kg$  and  $2\,\,kg$  are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of  $K.E.s$  of both the blocks is

A particle of mass $4\, m$ which is at rest explodes into three fragments. Two of the  fragments each of mass $m$ are found to move with a speed $v$ each in perpendicular directions. The total energy released in the process will be

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 force of $\left( {2\widehat i + 3\widehat j + 4\widehat k} \right)\,N$ acts on a body for $4\, sec$ and produces a displacement of $\left( {3\widehat i + 4\widehat j + 5\widehat k} \right)\,m$. The power used is :- …………… $\mathrm{W}$