$A$ bomb of mass $30 \, kg$ at rest explodes into two pieces of masses $18 \, kg$ and $12 \, kg$. The velocity of the $18 \, kg$ mass is $6 \, m/s$. The kinetic energy of the other mass is ....... $J$.

$A$ jet engine works on the principle of

$A$ 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

$A$ bomb of $12 \, kg$ explodes into two pieces of masses $4 \, kg$ and $8 \, kg$. The velocity of the $8 \, kg$ mass is $6 \, m/s$. The kinetic energy of the other mass is ............. $J$.

$A$ stationary body of mass $m$ explodes into $3$ parts having masses in the ratio $1 : 3 : 3$. The two parts having equal mass move at right angles to each other with a velocity of $15\,m/s$. What is the velocity of the third part?

$A$ buggy of mass $100\, kg$ is free to move on a frictionless horizontal track. Two men,each of mass $50\, kg$,are standing on the buggy,which is initially stationary. The men jump off the buggy with a velocity of $10\, m/s$ relative to the buggy. In one situation,the men jump one after the other. In another situation,the men jump simultaneously. What is the ratio of the recoil velocities of the buggy in the two cases?