$A$ bomb of mass $12\,kg$ at rest explodes into two fragments of masses in the ratio $1 : 3$. The $K.E.$ of the smaller fragment is $216\,J$. The momentum of the heavier fragment is (in $kg\cdot m/s$):

$A$ bomb of mass $3m \text{ kg}$ explodes into two pieces of mass $m \text{ kg}$ and $2m \text{ kg}$. If the velocity of the $m \text{ kg}$ mass is $16 \text{ m/s}$,the total kinetic energy released in the explosion is ................. $m \text{ J}$.

$A$ bullet of mass $m$ moving with velocity $v$ is fired into a wooden block of mass $M$. If the bullet remains embedded in the block,the final velocity of the system is:

$A$ ball is projected at $60^{\circ}$ from the horizontal at $200 \, m/s$. At the maximum height during its flight,it explodes into $3$ equal fragments. Out of these,one part travels at $100 \, m/s$ vertically up while another travels at $100 \, m/s$ vertically down. What will be the speed of the third part just after the explosion?

$A$ bullet is fired from a gun. If the gun recoils freely,the kinetic energy of the gun will be

$A$ projectile of mass $3m$ is moving at $40\, m/s$ at its highest point,where it breaks into two parts $m$ and $2m$. Mass $2m$ moves vertically up at $25\, m/s$. The other part will move at a speed of .................... $m/s$.