$A$ bomb at rest explodes into $3$ parts of the same mass. The momentum of two parts is $-3 p \hat{i}$ and $2 p \hat{j}$ respectively. The magnitude of the momentum of the third part is

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

$A$ cannon shell fired breaks into two equal parts at its highest point. If one part retraces its path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$,then

$A$ bomb is projected with $200\,m/s$ at an angle $60^o$ with the horizontal. At the highest point,it explodes into three particles of equal masses. One goes vertically upward with a velocity of $100\,m/s$,and the second particle goes vertically downward with the same velocity as the first. What is the velocity of the third particle?

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

$A$ 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