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

The motion of a rocket is based on the principle of conservation of

$A$ bomb of mass $16 \,kg$ explodes into two pieces of masses $4 \,kg$ and $12 \,kg$. The velocity of the $12 \,kg$ mass is $4 \,ms^{-1}$. The kinetic energy of the second piece (the $4 \,kg$ piece) is: (in $\,J$)

Two blocks $A$ and $B$ of masses $1\, kg$ and $2\, kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.$ of block $A$ to the $K.E.$ of block $B$ is:

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

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is: