$A$ steel ball of radius $2 \, cm$ is at rest on a frictionless surface. Another steel ball of radius $4 \, cm$ moving at a velocity of $81 \, cm/s$ collides elastically with the first ball. After the collision,the smaller ball moves with a speed of ............. $cm/s$.

For a perfectly elastic collision,the coefficient of restitution $e$ is

There is a head-on elastic collision between two particles moving in the same direction with speeds $5 \,m/s$ and $3 \,m/s$ respectively. After the collision,the velocity of the first particle becomes $4 \,m/s$ in the same direction. What is the velocity of the second particle?

Six steel balls of identical size are lined up along a straight frictionless groove. Two similar balls moving with a speed $V$ along the groove collide with this row on the extreme left end. Then:

$A$ block $A$ of mass $M$ moving with speed $u$ collides elastically with block $B$ of mass $m$ which is connected to block $C$ of mass $m$ with a spring. When the compression in the spring is maximum,the velocity of block $C$ with respect to block $A$ is (neglect friction):

As per the given figure,a small ball $P$ slides down the quadrant of a circle and hits another ball $Q$ of equal mass which is initially at rest. Neglecting the effect of friction and assuming the collision to be elastic,the velocity of ball $Q$ after the collision will be $............\,m/s$ $(g = 10\,m/s^2)$.