$A$ machine gun of mass $10\,kg$ fires $20\,g$ bullets at the rate of $180$ bullets per minute with a speed of $100\,m s^{-1}$ each. The recoil velocity of the gun is $.............\,m/s$.

State and explain the law of conservation of momentum for a system of particles.

$A$ block of mass $10 \ kg$ moving with a velocity of $5 \hat{i} \ m \ s^{-1}$ on a frictionless horizontal surface suddenly explodes into two pieces. If one piece with mass $4 \ kg$ moves with a velocity of $10 \hat{i} \ m \ s^{-1}$,then the velocity of the second piece is:

For a system to follow the law of conservation of linear momentum during a collision,the condition is:
$(1)$ Total external force acting on the system is zero.
$(2)$ Total external force acting on the system is finite and the time of collision is negligible.
$(3)$ Total internal force acting on the system is zero.

Two ice skaters $A$ and $B$ approach each other at right angles. Skater $A$ has a mass $30 \, kg$ and velocity $1 \, m/s$,and skater $B$ has a mass $20 \, kg$ and velocity $2 \, m/s$. They meet and cling together. Their final velocity of the couple is ............. $m/s$.

$A$ shell of mass $200\, g$ is ejected from a gun of mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $m/s$.