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 .............. $m/s$.

Object $A$ moving with velocity $v$ on a straight line collides with a stationary object $B$. After the collision,$B$ attains a velocity of $1.6v$. Assuming the collision is perfectly elastic,what percentage of $A$'s energy is transferred to $B$ during the collision?

Given below are two statements. One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$. Three identical spheres of same mass undergo one-dimensional motion as shown in the figure with initial velocities $v_{A} = 5 \ m/s$,$v_{B} = 2 \ m/s$,$v_{C} = 4 \ m/s$. If we wait sufficiently long for elastic collisions to happen,then $v_{A} = 4 \ m/s$,$v_{B} = 2 \ m/s$,$v_{C} = 5 \ m/s$ will be the final velocities.
Reason $(R)$: In an elastic collision between identical masses,two objects exchange their velocities. In the light of the above statements,choose the correct answer from the options given below:

$A$ sphere of mass $0.1 \ kg$ is attached to a string of length $1 \ m$. It is released from a horizontal position and collides with another sphere of equal mass $m$ at rest. Find the kinetic energy gained by the second sphere. The collision is perfectly elastic. (in $J$)

$A$ ball impinges directly on a similar ball at rest. If $1/4^{th}$ of the kinetic energy is lost by the impact, the value of the coefficient of restitution is:

Explain the special cases of elastic collision in one dimension.