$A$ body of mass $m$ moving with a constant velocity $v$ hits another body of the same mass that is at rest. If the two bodies stick together after the collision,the velocity of the compound body is:

$A$ bullet weighing $10 \,g$ and moving with a velocity $300 \,m/s$ strikes a $5 \,kg$ block of ice and gets embedded in it. The ice block is kept on a smooth surface. The speed of the block after the collision is ........ $cm/s$.

$A$ bullet of mass $m$ moving with velocity $v$ strikes a block of mass $M$ at rest and gets embedded into it. The kinetic energy of the composite block will be

$A$ body of mass $m$ moves with velocity $v$ in the East direction,and another body of the same mass moves with velocity $v$ in the North direction. After they collide and stick together,what is the combined velocity of the resulting body of mass $2m$?

$A$ body of mass $m$ moving with velocity $v$ collides head-on with another body of mass $2m$ which is initially at rest. If the collision is perfectly inelastic,what is the loss in kinetic energy of the system?

$A$ bag (mass $M$) hangs by a long thread and a bullet (mass $m$) comes horizontally with velocity $v$ and gets caught in the bag. Then for the combined (bag $+$ bullet) system