$A$ 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?

An isolated rail car of mass $M$ is moving along a straight,frictionless track at an initial speed $v_0$. The car is passing under a bridge when a crate filled with $N$ bowling balls,each of mass $m$,is dropped from the bridge into the bed of the rail car. The crate splits open and the bowling balls bounce around inside the rail car,but none of them fall out. Is the momentum of the rail car $+$ bowling balls system conserved in this collision?

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

$A$ vessel at rest explodes into three pieces. Two pieces having equal masses $m$ fly off perpendicular to one another with the same velocity $30 \, m/s$. The third piece has three times the mass of each of the other pieces. The magnitude and direction of the velocity of the third piece will be:

$A$ body of mass $5 \,kg$ explodes at rest into three fragments with masses in the ratio $1 : 1 : 3$. The fragments with equal masses fly in mutually perpendicular directions with speeds of $21 \,m/s$. The velocity of the heaviest fragment will be

$A$ body of mass $M$ at rest explodes into three pieces,two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3 \, m/s$ and $4 \, m/s$ respectively. The third piece will be thrown off with a velocity of .......... $m/s$