$A$ body of mass $m$ moving with speed $3 \ m/s$ collides with a body of mass $2m$ at rest. The coalesced mass will start to move with a speed of (in $m/s$)

$A$ bullet of mass $m$ moving with a speed $v$ strikes a wooden block of mass $M$ and gets embedded into the block. The final speed is

$A$ 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 of mass $a$ and velocity $b$ is fired into a large block of mass $c$. The final velocity of the system is

$A$ 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,

$A$ bag of sand of mass $9.8 \, kg$ is suspended by a rope. $A$ bullet of mass $200 \, g$ travelling with a speed of $10 \, ms^{-1}$ gets embedded in it. The loss of kinetic energy will be $... J$.