$A$ body of mass $m_1$ is moving with a velocity $V$. It collides with another stationary body of mass $m_2$. They get embedded. At the point of collision,the velocity of the system

$A$ body of mass $2 \, kg$ moving with a velocity $(\hat{i} + \hat{j} + \hat{k}) \, m/s$ collides with another body of mass $5 \, kg$ moving with velocity $(\hat{i} - 2\hat{j} + 3\hat{k}) \, m/s$. If they stick together, the velocity (in $m/s$) of the composite body is:

$A$ particle of mass $m$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$ direction with speed $v$. If the collision is perfectly inelastic,the percentage loss in the energy during the collision is close to $..........\%$

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.

$A$ bullet of mass $m$ is fired horizontally with a velocity $u$ into a sandbag placed on a truck. If the mass of the truck is $M$, what will be the velocity of the truck after the collision?

$A$ 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 $... J$.