A ball after falling from a height of  $10\,\,m$  strikes the roof of a lift which is descending down with a velocity of  $1\,\,m/s$ . The recoil velocity of the ball will be ............. $\mathrm{m}/ \mathrm{s}$

Body $A$ of mass $4 \;\mathrm{m}$ moung with speed $u$ collides with another body $B$ of mass $2\; \mathrm{m}$, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body $A$ is

A body of mass $M$ moves with velocity $v$ and collides elastically with a another body of mass $m$ ($M>>m$) at rest then the velocity of body of mass $m$ is

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:

A particle of mass $m$ moving in the $x$ direction with speed $2 v$ is hit by another particle of mass $2 m$ moving in the $y$ direction with speed $v$. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to $..........\%$

Three particles each of mass $m$ are located at the vertices of an equilateral triangle $ABC$. They start moving with equal speeds $v$ each along the medians of the triangle and collide at its centroid $G$. If after collision, $A$ comes to rest and $B$ retraces its path along $GB,$ then $C$