An object of mass $m _{1}$ collides with another object of mass $m _{2}$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m _{2}: m _{1}$ is

Two masses ${m_A}$and ${m_B}$moving with velocities ${v_A}$and ${v_B}$in opposite directions collide elastically. After that the masses ${m_A}$and ${m_B}$move with velocity ${v_B}$and ${v_A}$respectively. The ratio $ \frac{m_A}{m_B} =$

A heavy body moving with a velocity $30\, m/s$ and another small object at rest undergo  an elastic collision. The latter will move with a velocity of .............. $\mathrm{m}/ \mathrm{s}$

Three different projectiles, each with the same mass, are fired with speed $v$ at a wall. In case $A,$ the projectile bounces straight back with speed $v.$ In case $B$, the projectile sticks to the wall. In case $C$, the projectile crashes through the wall and emerges with half its original speed. These three cases are shown here.

Place the impulse exerted by the wall on the projectile in each of these three cases in the correct order.

In an elastic collision of two billiard balls which of the following quantities is not conserved during the short time of collision

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$ : Body $'P'$ having mass $M$ moving with speed $'u'$ has head-on collision elastically with another body $'Q'$ having mass $'m'$ initially at rest. If $m< < M,$ body $'Q'$ will have a maximum speed equal to $'2u'$ after collision.

Reason $R$ : During elastic collision, the momentum and kinetic energy are both conserved.

In the light of the above statements, choose the most appropriate answer from the options given below: