Two billiard balls undergo a head-on collision. Ball $1$ is twice as heavy as ball $2$. Initially,ball $1$ moves with a speed $v$ towards ball $2$ which is at rest. Immediately after the collision,ball $1$ travels at a speed of $v/3$ in the same direction. What type of collision has occurred?

In a carrom-board game,the striker and the coins are identical and of mass $m$. In a particular hit,the coin is hit when it is placed close to the edge of the board as shown in the figure,such that the coin travels parallel to the edge after the collision. If the striker is moving with speed $v$ before the strike,then the net impulse on the striker during the collision,if it moves perpendicular to the edge after the collision,is (assume all collisions to be perfectly elastic):

$A$ $2\, kg$ block moving with $10\, m/s$ strikes a spring of constant $\pi^2\, N/m$ attached to a $2\, kg$ block at rest kept on a smooth floor. The velocity of the rear $2\, kg$ block after it separates from the spring will be ..... $m/s$.

$A$ heavy body moving with a velocity $30\, m/s$ and another small object at rest undergo an elastic collision. The latter will move with a velocity of .............. $m/s$.

Six identical balls are lined up in a straight groove on a horizontal frictionless surface. Two similar balls,each moving with a velocity $v$,collide elastically with the row of $6$ balls from the left. What will happen?

$A$ ball $A$ of mass $m$ moving along the positive $x$-direction with kinetic energy $K$ and momentum $p$ undergoes an elastic head-on collision with a stationary ball $B$ of mass $M$. After the collision,the ball $A$ moves along the negative $x$-direction with kinetic energy $K/9$. The final momentum of $B$ is: