$A$ ball after falling from a height of $10 \ m$ strikes the roof of a lift which is descending with a velocity of $1 \ m/s$. The recoil velocity of the ball will be ............. $m/s$. (Assume elastic collision)

Two balls of mass $5 \ kg$ are moving in opposite directions with the same speed of $5 \ m/s$. They undergo a head-on elastic collision. Find the final velocity of the balls in $m/s$.

$A$ ball moving with velocity $V$ undergoes a perfectly elastic collision with an identical ball moving in the opposite direction with velocity $2V$. Taking the direction of $V$ as positive,find the velocities of both balls after the collision.

$A$ neutron with velocity $v$ and kinetic energy $E$ collides head-on with a stationary nucleus of mass number $A$. What is the fraction of kinetic energy lost by the neutron?

$A$ heavy body moving with a velocity of $6\,ms^{-1}$ collides elastically with a light body (whose mass is half of the mass of the heavy body) at rest. The velocity of the light body will be (in $ms^{-1}$):

$A$ mass $M$ moving with a certain speed $V$ collides elastically with another stationary mass $m$. After the collision,the masses $M$ and $m$ move with speeds $V^{\prime}$ and $v$,respectively. All motion is in one dimension. Then,