$A$ bomb at rest explodes into three parts of equal mass. If the momentum of two parts are $-2 p \hat{i}$ and $p \hat{j}$,find the magnitude of momentum of the third part.

$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is:

$A$ stationary body explodes into two parts of masses $M_{1}$ and $M_{2}$. They move in opposite directions with velocities $v_{1}$ and $v_{2}$. The ratio of their kinetic energies is

$A$ 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 $m/s$?

$A$ bomb at rest explodes into three fragments $X, Y$ and $Z$. Each one of them has the same mass. Which of the following correctly describes the motion of the fragments?

Three particles of masses $10 \ g, 20 \ g$ and $40 \ g$ are moving with velocities $10 \hat{i}, 10 \hat{j}$ and $10 \hat{k} \ m/s$ respectively. If due to some mutual interaction,the first particle comes to rest and the velocity of the second particle becomes $(3 \hat{i} + 4 \hat{j}) \ m/s$,then the velocity of the third particle is: