After on 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

A bag of sand of mass $M$ is suspended by a string. A bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is

A car is moving on a straight horizontal road with a speed $v.$ If the coefficient of friction between the tyres and the road is $\mu ,$ the shortest distance in which the car can be stopped is

If a spring extends by $x$ on loading then energy stored by the spring is ($T$ is tension in spring, $K$ is spring constant)

A frictionless track $ABCDE$ ends in a circular loop of radius $R$ .A body slides down the track from point $A$ which is at a height $h = 5\, cm$. Maximum value of $R$ for the body to successfully complete the loop is .................. $\mathrm{cm}$

$Assertion$ : If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.
$Reason$ : During collision intermolecular space decreases and hence elastic potential energy increases