$A$ ball of mass $m$ moving with velocity $V$ makes a head-on elastic collision with a ball of the same mass moving with velocity $2V$ towards it. Taking the direction of $V$ as positive,the velocities of the two balls after the collision are:

Ball $A$ moving at $12 \ m/s$ collides elastically with ball $B$ at rest as shown in the figure. If both balls have the same mass,what is the final velocity of ball $A$ after the collision (in $m/s$)? (Assume the collision is two-dimensional and the angle of incidence is $60^\circ$ with the vertical axis).

$A$ 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 ............. $cm/s$.

$A$ ball hits the floor and rebounds. For this elastic collision case,which of the following is true?

Explain the special cases of elastic collision in one dimension.

$A$ ball of mass $m$ moving with speed $u$ undergoes a head-on elastic collision with a stationary ball of mass $nm$. What is the fraction of the kinetic energy transferred to the heavier ball?