Velocity of the ball $A$ after collision with the ball $B$ as shown in the figure is ............. $m/s$. (Assume perfectly inelastic and head-on collision)

$A$ mass $m$ moving horizontally (along the $x-$axis) with velocity $v$ collides and sticks to a mass of $3m$ moving vertically upward (along the $y-$axis) with velocity $2v$. The final velocity of the combination is

$A$ body of mass $m$ moving with a constant velocity $v$ hits another body of the same mass moving with the same velocity $v$ but in the opposite direction and sticks to it. The velocity of the compound body after collision is

$A$ particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2m$. After collision,they stick together and continue to move together with velocity ........

$A$ metal ball of mass $2 \,kg$ moving with a velocity of $36 \,km/h$ has a head-on collision with a stationary ball of mass $3 \,kg$. If after the collision,the two balls move together,the loss in kinetic energy due to the collision is ........ $J$.

$A$ bag of sand of mass $M$ is suspended by a string. $A$ bullet of mass $m$ is fired at it with velocity $v$ and gets embedded into it. The loss of kinetic energy in this process is