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 files off with $4 \,m s^{-1}$ speed, then its mass is ……… $kg$

A shell of mass $0.020\; kg$ is fired by a gun of mass $100\; kg$. If the muzzle speed of the shell is $80 \;m s^{-1}$, what is the recoil speed in $m/s$ of the gun ?

An object of mass $3\,m$ splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is

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 ………. $m/s$

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