A body of mass m having an initial velocity $v$, makes head on collision with a stationary body of mass $M$. After the collision, the body of mass $m$ comes to rest and only the body having mass $M$ moves. This will happen only when

$A$ chain of length $L$ and mass $m$ is placed upon a smooth surface. The length of $BA$ is $L-b$. Calculate the velocity of the chain when its end reaches $B$.

A light particle moving horizontally with a speed of $12\  m/s$ strikes a very heavy block moving in the same direction at $10\  m/s$. The collision is one-dimensional and elastic. After the collision, the particle will

A ball of mass $200\,g$ rests on a vertical post of height $20\,m$. A bullet of mass $10\,g$, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of initial velocity of the bullet will be $............m/s$ (if $\left.g =10 m / s ^2\right)$

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 correct statements is :

Select the false statement