A body $x$ with a momentum $p$ collides with another identical stationary body $y$ one dimensionally. During the collision $y$ gives an impulse $J$ to body $x$. Then coefficient of restitution is

Two balls $A$ and $B$ having masses $1\, kg$ and $2\, kg$, moving with speeds $21\, m/s$ and $4\, m/s$ respectively in opposite direction, collide head on. After collision Amoves with a speed of $1\, m/s$ in the same direction, then the coefficient of restitution is

An object of mass $M_1$ moving horizontally with speed $u$ collides elastically with another object of mass $M_2$ at rest. Select correct statement.

A particle of mass $m$ with an initial velocity $u\hat i$ collides perfectly elastically with a mass $3m$ at rest. It moves with a velocity $v\hat j$ after collision, then, $v$ is given by

A rubber ball is dropped from a height of $5 \,m$ on a planet where the acceleration due to gravity is not known. On bouncing, it rises to $1.8\, m$. The ball loses its velocity on bouncing by a factor of

A ball is dropped from a height of $20\,m$. If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of $.............m$.