$A$ 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 $\,ms^{-1}$)

$A$ block of mass $4 m$ travelling at a velocity $v_1$ in the $x$-direction on a frictionless horizontal plane makes a head-on collision with another block of mass $2 m$ travelling in the opposite direction with a velocity $v_2$. After the collision,both blocks travel as a single block along the $x$-direction with a final velocity $5 v_2$. The ratio of velocities $\frac{v_1}{v_2}$ is

$A$ bullet strikes against a wooden block and is embedded in it,the nature of collision is

$A$ metal ball of mass $2 \,kg$ moving with a speed of $10 \,ms^{-1}$ has a head-on collision with a stationary ball of mass $3 \,kg$. If after the collision, both the balls move together, then the loss in kinetic energy due to the collision is: (in $\,J.$)

$A$ block of mass $0.50 \ kg$ is moving with a speed of $2.00 \ m/s$ on a smooth surface. It strikes another mass of $1.00 \ kg$ at rest and then they move together as a single body. The energy loss during the collision is ............. $J$.

$A$ particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2m$ and sticks to it. What is the combined velocity of the system?