$A$ spacecraft of mass $M$ moving with velocity $v$ suddenly breaks into two pieces of equal mass $m$. After the explosion,one of the masses $m$ becomes stationary. What is the velocity of the other part of the craft?

An explosion blows a stationary rock into three parts. Two parts of masses $1 \,kg$ and $2 \,kg$ move at right angles to one another with velocities $12 \,ms^{-1}$ and $8 \,ms^{-1}$, respectively. If the velocity of the third part is $4 \,ms^{-1}$, the mass of the rock is (in $\,kg$)

$A$ body of mass $0.25 \, kg$ is projected with a muzzle velocity of $100 \, m/s$ from a tank of mass $100 \, kg$. What is the recoil velocity of the tank in $m/s$?

$A$ wagon weighing $1000\, kg$ is moving with a velocity of $50\, km/h$ on smooth horizontal rails. $A$ mass of $250\, kg$ is dropped into it. The velocity with which it moves now is ......... $km/h$.

$A$ particle of mass $4\, m$ which is at rest explodes into three fragments. Two of the fragments,each of mass $m$,are found to move with a speed $v$ each in perpendicular directions. The total energy released in the process 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