A ball of mass $ m$  moving with velocity $V$, makes a head on elastic collision with a ball of the same mass moving with velocity $2V$ towards it. Taking direction of $V$ as positive velocities of the two balls after collision are

A ball of mass $m$ moving with velocity $v$ collides head-on with the second ball of mass $m$ at rest. If the coefficient of restitution is $e$ and velocity of first ball after collision is $v_1$ and velocity of second ball after collision is $v_2$ then

A billiard ball moving with a speed of $5 \,m/s$ collides with an identical ball originally at rest. If the first ball stops after collision, then the second ball will move forward with a speed of ...........  $m{s^{ - 1}}$

Body of mass $M$ is much heavier than the other body of mass $m$. The heavier body with speed $v$ collides with the lighter body which was at rest initially elastically. The speed of lighter body after collision is

A ball of mass $m$ strikes the inclined face of the wedge normally with speed $v_0$. The wedge is at rest on a rough horizontal surface before collision. The conservation of momentum is applicable for the event of collision for

$(i)$ $m$ as system, along $Y'$
$(ii) $ $M$ as system, along $Y'$
$(iii)$ $(M + m)$ as system, along $X$
$(iv)$  $(M + m)$ as system, along $Y$
Which of the following is correct?

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