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)

Two identical particles are moving with same velocity $v$ as shown in figure. If the  collision is completely inelastic then

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 body of mass $2\, kg$ slides down a curved track which is quadrant of a circle of radius $1$ metre. All the surfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is ..............  $\mathrm{m} / \mathrm{s}$

A container of mass $m$ is pulled  by a constant force in which a second block of same mass $m$ is placed connected to the wall by a mass-less spring of constant $k$ . Initially the spring is in its natural length. Velocity of the container at the instant when compression in spring is maximum for the first time

An object has momentum $p$ & kinetic energy $E$. If its momentum becomes $2\,p$ then  its kinetic energy will be :-