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
${\left( {\frac{A}{B}} \right)^{1/6}}$
${\left( {\frac{{2A}}{B}} \right)^{1/6}}$
${\left( {\frac{A}{{2B}}} \right)^{1/6}}$
None of these
The kinetic energy $K$ of a particle moving in a straight line depends upon the distance $s$ as $K = as^2$. The force acting on the particle is
Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on horizontal portion $MN$. The ratio of the heights attained by $A$ and $B$ after collision will be (neglect friction)
$F = 2x^2 - 3x - 2$. Choose correct option
After head on elastic collision between two balls of equal masses , one is observed to have a speed of $3\,\,m/s$ along positive $x-$ axis and the other has a speed of $2\,\,m/s$ along negative $x$ axis. The original velocities of the balls are
$ABCDE$ is a channel in the vertical plane, part $BCDE$ being circular with radius $r$ . A block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is