$A$ spacecraft of mass $M$ moves with velocity $V$ in free space. It explodes and breaks into two pieces. If after the explosion,a piece of mass $m$ comes to rest,what will be the velocity of the other piece of the spacecraft?

$A$ bullet of mass $0.1\,kg$ is fired with a speed of $100\,m/s$. The mass of the gun is $50\,kg$. The recoil velocity of the gun is ........ $m/s$.

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?

$A$ stationary body explodes into two parts of masses $M_{1}$ and $M_{2}$. They move in opposite directions with velocities $v_{1}$ and $v_{2}$. The ratio of their kinetic energies is

$A$ body of mass $M$ moving with velocity $V$ explodes into two equal parts. If one part comes to rest and the other part moves with velocity $v_{0}$,what would be the value of $v_{0}$?

$A$ 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 .............. $m/s$.