$A$ particle of mass $m$ moving with a velocity $\vec{V}$ makes a head-on elastic collision with another particle of the same mass initially at rest. The velocity of the first particle after the collision will be:

$A$ neutron travelling with a velocity $v$ and kinetic energy $E$ collides perfectly elastically head-on with the nucleus of an atom of mass number $A$ at rest. The fraction of total energy retained by the neutron is

$A$ mass $M$ moving with a certain speed $V$ collides elastically with another stationary mass $m$. After the collision,the masses $M$ and $m$ move with speeds $V^{\prime}$ and $v$,respectively. All motion is in one dimension. Then,

Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite directions with equal speeds. If their masses are $m_A$ and $m_B$ respectively,then:

$A$ smooth sphere of mass $M$ moving with velocity $u$ directly collides elastically with another sphere of mass $m$ at rest. After collision,their final velocities are $V$ and $v$ respectively. The value of $v$ is

$Assertion$ : In an elastic collision of two billiard balls,the total kinetic energy is conserved during the short time of oscillation of the balls (i.e.,when they are in contact).
$Reason$ : Energy spent against friction does not follow the law of conservation of energy.