$A$ ball is dropped from a height of $80 \ m$ on a surface which is at rest. Find the height attained by the ball after the $2^{nd}$ collision if the coefficient of restitution is $e = 0.5$.

$A$ neutron moving with velocity $u$ collides elastically with an atom of mass number $A$. If the collision is head-on and the initial kinetic energy of the neutron is $E$, then the final kinetic energy of the neutron after the collision is:

Which of the following is not a perfectly inelastic collision?

$Assertion$: $n$ small balls each of mass $m$ collide elastically each second on a surface with velocity $u$. The force experienced by the surface is $2mnu$.
$Reason$: On elastic collision,the ball rebounds with the same velocity.

$A$ ball of $0.4 \, kg$ mass and a speed of $3 \, m/s$ has a head-on,completely elastic collision with a $0.6 \, kg$ mass initially at rest. Find the speeds of both balls after the collision:

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. What were the original velocities of the balls?