$A$ neutron with velocity $v$ and kinetic energy $E$ collides head-on with a stationary nucleus of mass number $A$. What is the fraction of kinetic energy lost by the neutron?

Two balls $X(2 \ kg)$ and $Y(4 \ kg)$ approach each other with equal speeds of $10 \ ms^{-1}$. If the collision is perfectly elastic,then the new velocities of balls $X$ and $Y$ are respectively

$Assertion$ : If collision occurs between two elastic bodies,their kinetic energy decreases during the time of collision.
$Reason$ : During collision,intermolecular space decreases and hence elastic potential energy increases.

An object $A$ of mass $20 \ kg$ and travelling at $20 \ m \ s^{-1}$ crashes into another object $B$ of mass $200 \ kg$ and travelling at $10 \ m \ s^{-1}$, in the same direction. After the collision, object $A$ bounces back in the opposite direction at a speed of $10 \ m \ s^{-1}$. The speed of the object $B$ after the collision is: (in $m \ s^{-1}$)

$A$ ball of mass $0.1 \ kg$ undergoes a head-on collision with a stationary ball of unknown mass. If the $0.1 \ kg$ ball rebounds with $1/3$ of its original speed,the mass of the second ball is .......... $kg$.

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