$A$ 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 $, m$)

$A$ particle of mass $4m$ explodes into three pieces of masses $m, m$ and $2m$. The equal masses move along the $X$-axis and $Y$-axis with velocities $4 \text{ ms}^{-1}$ and $6 \text{ ms}^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

$A$ body is moving with a velocity $v$ and breaks up into two equal parts. One of the parts retraces its path with velocity $v$. Then the velocity of the other part is:

$A$ man of mass $m$ is standing on a cart of mass $2m$. Initially, the cart is at rest. The man jumps horizontally with a relative velocity $u$ with respect to the cart. The work done by the internal forces of the man during the process of jumping will be:

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. What is the average speed of the rail car $+$ bowling balls system some time after the collision?

Why is the law of conservation of linear momentum considered fundamental and universal?