In an explosion,a body breaks up into two pieces of unequal masses. In this process:

$A$ bullet of mass $5 \,g$ is shot from a gun of mass $5 \,kg$. The muzzle velocity of the bullet is $500 \,m/s$. The recoil velocity of the gun is ........... $m/s$.

$A$ body at rest explodes into two pieces of unequal mass. The parts will move

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \, kg$ moves with a speed of $12 \, m s^{-1}$ and the second part of mass $2 \, kg$ moves with $8 \, m s^{-1}$ speed. If the third part flies off with $4 \, m s^{-1}$ speed,then its mass is ......... $kg$.

$A$ jet engine works on the principle of

$A$ projectile is fired with velocity $u$ at an angle $\theta$ with the horizontal. At the highest point of its trajectory,it splits into three segments of masses $m, m$,and $2m$. The first part falls vertically downward with zero initial velocity,and the second part returns via the same path to the point of projection. The velocity of the third part of mass $2m$ just after the explosion will be: