During an elastic collision between two bodies,which of the following statements are correct?
$I$. The initial kinetic energy is equal to the final kinetic energy of the system.
$II$. The linear momentum is conserved.
$III$. The kinetic energy during $\Delta t$ (the collision time) is not conserved.

Consider the following statements $A$ and $B$ and identify the correct answer:
$A$. In an elastic collision,if a body suffers a head-on collision with another of the same mass at rest,then the first body comes to rest while the other starts moving with the velocity of the first one.
$B$. Two bodies of equal mass suffering a head-on elastic collision merely exchange their velocities.

After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3 \, m/s$ along the positive $x$-axis and the other has a speed of $2 \, m/s$ along the negative $x$-axis. The original velocities of the balls are:

$A$ body of mass $2 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction with one-fourth of its original speed. The mass of the second body which collides with the first body is ............... $kg$.

Which one of the following statements does not hold good when two balls of masses $m_1$ and $m_2$ undergo elastic collision?

$A$ body of mass $5 \ kg$ makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to $\frac{1}{10}$ th of its original velocity. Then the mass of the second body is (in $kg$)