$A$ bomb of mass $9 \text{ kg}$ explodes into two pieces of mass $3 \text{ kg}$ and $6 \text{ kg}$. The velocity of mass $3 \text{ kg}$ is $16 \text{ m/s}$. The kinetic energy of mass $6 \text{ kg}$ (in joule) is

$A$ 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

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. If one of those parts having mass $m/6$ remains stationary,find the velocity of the other part.

For a system to follow the law of conservation of linear momentum during a collision, the condition is:
$(1)$ Total external force acting on the system is zero.
$(2)$ Total external force acting on the system is finite and the time of collision is negligible.
$(3)$ Total internal force acting on the system is zero.

$A$ mass of $1 \; kg$ is thrown up with a velocity of $100 \; m/s$. After $5 \; s$,it explodes into two parts. One part of mass $400 \; g$ comes down with a velocity of $25 \; m/s$. Calculate the velocity of the other part.

The law of conservation of linear momentum is derived by using which of Newton's laws?