$A$ bullet of mass $m$ is fired from a gun of mass $M$. If the velocity of the bullet is $v$,what will be the recoil velocity of the gun?

In an explosion,a body breaks up into two pieces of unequal masses. In this process:

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. If one of those parts having mass $m/6$ remains stationary,find the velocity of the other part.

$10m$ is the total mass of a cannon that includes all shells. Initially, the cannon is moving with a velocity of $10 \ m/s$ along a horizontal frictionless path. If the cannon fires $n$ shells of mass $m$ in the direction of motion of the cannon one by one with velocity $u$ with respect to the ground, which of the following statements is correct? (Neglect any friction force)

State the law of conservation of total linear momentum for a system of particles.

$A$ $300 \ kg$ trolley carrying a $25 \ kg$ sandbag is moving on a frictionless track with a uniform speed of $27 \ km/hr$. After some time,sand starts leaking out of the bag at a rate of $0.05 \ kg/s$ and falls onto the floor of the trolley. Find the speed of the trolley in $km/hr$ when the sandbag is completely empty.