Four particles $A, B, C$ and $D$ of equal mass are placed at four corners of a square.  They move with equal uniform speed $v$ towards the intersection of  the diagonals. After  collision, $A$ comes to rest, $B$ traces its path back with same speed and $C$ and $D$ move with equal speeds. What is the velocity of $C$ after collision

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 

Work done in time $t $ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time ${t_1}$ as a function of time $t$ is given by

A spring of spring constant $5 \times 10^3\, N/m$ is stretched initially by $5\,cm$ from the unstretched position. Then the work required to stretch it further by another $5\, cm$ is ………….. $\mathrm{N}$  $-$ $\mathrm{m}$

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to