$A$ 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

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 ......... $kg$.

From a stationary tank of mass $125000 \ lb$,a small shell of mass $25 \ lb$ is fired with a muzzle velocity of $1000 \ ft/sec$. The tank recoils with a velocity of ............ $ft/sec$.

$A$ shell of mass $M$ initially at rest suddenly explodes into three fragments. Two of these fragments are of mass $M/4$ each, which move with velocities $3 \text{ m/s}$ and $4 \text{ m/s}$ respectively in mutually perpendicular directions. The magnitude of the velocity of the third fragment is: (in $\text{ m/s}$)

$A$ $1 \; kg$ stationary bomb explodes into three parts having mass ratio $1:1:3$. The parts with equal mass move in perpendicular directions with a velocity of $30 \; m/s$. What is the velocity of the third (heavier) part?

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be