The law of conservation of linear momentum is derived by using which of Newton's laws?

$A$ ball of mass $m = 60 \text{ g}$ is shot with speed $v_0 = 22 \text{ m/s}$ into the barrel of a spring gun of mass $M = 240 \text{ g}$,which is initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. The speed of the spring gun after the ball stops relative to the barrel is:

$A$ bomb of mass $10\, kg$ explodes into two pieces of masses $4\, kg$ and $6\, kg$. If the kinetic energy of the $4\, kg$ piece is $200\, J$,find the kinetic energy of the $6\, kg$ piece.

If the resultant of all the external forces acting on a system of particles is zero,then from an inertial frame,one can surely say that

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When both the persons jump simultaneously with $u_{rel}$ with respect to the trolley,then the velocity of the trolley is

$A$ 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 $.............\,m/s$.