Two perfectly elastic particles $P$ and $Q$ of equal mass travelling along the line joining them with velocities $15\, m/sec$ and $10\, m/sec$. After collision, their velocities respectively (in m/sec) will be

Assertion $(A)$: In an elastic collision between two bides, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Reason $(R)$: In elastic collision, the linear momentum of the system is conserved.

Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on horizontal portion $MN$. All surfaces are smooth. The ratio of heights attained by $A$ and $B$ after collision will be(Neglect energy loss at $M$ & $N$)

A particle $P$ moving with speed $v$  undergoes a head -on elastic collision with another particle $Q$ of identical mass but at rest. After the collision

A ball is projected vertically down with an initial velocity from a height of $ 20 m$  onto a horizontal floor. During the impact it loses $ 50\% $ of its energy and rebounds to the same height. The initial velocity of its projection is ............ $\mathrm{m} / \mathrm{s}^{-1}$

Six steel balls of identical size are lined up long a straight frictionless groove. Two similar balls moving with a speed $V$ along the groove collide with this row on the extreme left hand then