$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ particle of mass $m$ strikes the rod at one end with a velocity $v$ perpendicular to the rod. If the particle comes to rest after the collision,the velocity of the center of mass of the rod after the collision is:

$A$ ball hits the floor and rebounds after an inelastic collision. In this case:

Two identical balls $P$ and $Q$ moving in the $x-y$ plane collide at the origin $(x=0, y=0)$ of the coordinate system. Their velocity components just before the moment of impact were,for ball $P$,$v_x = 6 \ m/s, v_y = 0$; for ball $Q$,$v_x = -5 \ m/s, v_y = 2 \ m/s$. As a result of the collision,ball $P$ comes to rest. The velocity components of ball $Q$ just after the collision will be:

$A$ ball is dropped from a height of $5\,m$. The time after which the ball stops rebounding,if the coefficient of restitution between the ball and the ground is $e = 1/2$,is ............. $s$.

$A$ ball kept at $20 \,m$ height falls freely in a vertically downward direction and hits the ground. The coefficient of restitution is $0.4$. What is the velocity of the ball after the first rebound (in $\,ms^{-1}$)? $\left[g=10 \,ms^{-2}\right]$

$A$ $1.0 \ kg$ ball drops vertically onto a floor from a height of $25 \ cm$. It rebounds to a height of $4 \ cm$. The coefficient of restitution for the collision is