$A$ system of $N$ particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system?

$A$ 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:

$A$ projectile of mass $m$ is projected from ground with a speed of $50 \, m/s$ at an angle of $53^{\circ}$ with the horizontal. It breaks up into two equal parts at the highest point of the trajectory. One particle comes to rest immediately after the explosion. The distance between the pieces of the projectile when they reach the ground is: (in $, m$)

$A$ man of $50 \,kg$ is standing at one end of a boat of length $25 \,m$ and mass $200 \,kg$. If he starts running and when he reaches the other end, he has a velocity $2 \,ms^{-1}$ with respect to the boat. The final velocity of the boat is : (in $ms^{-1}$ )

$A$ spacecraft of mass $M$ is moving with a velocity $V$. It suddenly breaks into two parts. One part of mass $m$ comes to rest. What will be the velocity of the other part?

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