$A$ 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)

$A$ ball initially at rest is hit by another identical ball moving with some velocity as shown. Find the angle $\theta_2$ if the surface is without friction and the collision is perfectly elastic. $......^{\circ}$

$A$ body of mass $30 \ kg$ moving with a velocity $20 \ ms^{-1}$ undergoes a one-dimensional elastic collision with another ball of the same mass moving in the opposite direction with a velocity of $30 \ ms^{-1}$. After the collision,the velocities of the first and second bodies respectively are:

Explain the special cases of elastic collision in one dimension.

$A$ steel sphere of radius $1.2 \ cm$ collides with a second steel sphere at rest. If the collision is elastic and after the collision the first sphere continues to move in its initial direction with a velocity of $\frac{7}{9}$ times its initial velocity,then the radius of the second sphere is (in $cm$)

Four smooth steel balls of equal mass at rest are free to move along a straight line without friction. The first ball is given a velocity of $0.4\, m/s$. It collides head-on with the second elastically,the second one similarly with the third and so on. The velocity of the last ball is .............. $m/s$.