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)

Two identical balls are suspended side by side by two long strings. One ball is pulled aside so that its center of gravity rises by a vertical distance $h$. It is then released and undergoes a perfectly inelastic collision with the other ball. What is the vertical distance to which the center of gravity of the combined system rises?

Find the correct option based on the two statements given below.
Statement-$1$ : Two particles moving in the same direction do not lose all their energy in a perfectly inelastic collision.
Statement-$2$ : The law of conservation of linear momentum is obeyed for all types of collisions.

$A$ body of mass $3 \,kg$ is moving with a velocity of $8 \,ms^{-1}$ collides head-on with another body of mass $1 \,kg$, moving in the opposite direction with a velocity of $4 \,ms^{-1}$. After the collision, if the two bodies stick together and move, they move with a common velocity: (in $\,ms^{-1}$)

$A$ bullet is fired from a gun. It hits a solid block resting on a frictionless surface,gets embedded into it,and both move jointly. In this process,

$A$ 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 ........ $J$.