The potential energy of a particle oscillating along $x-$ axis is given as $U =20+ (x - 2)^2$ where $U$ is in $joules$ and $x$ in $meters$ . Total mechanical energy of the particle is $36 \,J$. Maximum kinetic energy of the particle is ............... $\mathrm{J}$

A sphere of mass $m$ travelling at constant speed $v$ strike another sphere of same mass. If  coefficient of restitution is $e$, then ratio of velocity of both spheres just after collision is :-

Work equal to $25\,J$ is done on a mass of $2\,kg$ to set it in motion. If whole of it is used to increase the kinetic energy then velocity acquired by the mass is ............ $\mathrm{m}/ \mathrm{s}$

In an elastic collision of two particles the following quantity is conserved

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:

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