Momentum of a System of Particles

A bomb of mass $12 \mathrm{kg}$ at rest explodes into two fragments of masses in the ratio $1:3$. The kinetic energy of the smaller fragment is $216 \mathrm{J}$. The momentum of the heavier fragment is (in $\mathrm{kg} \mathrm{m} {\mathrm{s}}^{-1}$)

A body of mass $(4 \mathrm{m})$ is lying in $\mathrm{x}-\mathrm{y}$. plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass $\left(\mathrm{m}\right)$ move perpendicular to each other with equal speeds $\left(\mathrm{v}\right)$. The total kinetic energy generated due to explosion is
 

A bomb of mass $3.0 \text{kg}$ explodes in air into two pieces of masses $2.0\text{ kg}$ and $1.0 \text{kg}$.The smaller mass goes at a speed of $80 {\text{ms}}^{-1}$. The total energy imparted to the two fragments is

A bomb of mass $30 \mathrm{kg}$ at rest explodes into two pieces of masses $18 \mathrm{kg}$ and $12 \mathrm{kg}$. The velocity of $18 \mathrm{kg}$ mass is $6 {\mathrm{ms}}^{-1}$. The kinetic energy of the other mass is

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, $1 \mathrm{kg}$ first part moving with a velocity of $12 \mathrm{m} {\mathrm{s}}^{-1}$ and $2 \mathrm{kg}$ second part moving with a velocity of $8 \mathrm{m} {\mathrm{s}}^{-1}$. If the third part flies off with a velocity of $4 \mathrm{m} {\mathrm{s}}^{-1}$, its mass would be:

A shell explodes in a region of negligible gravitational field, giving out $n$ fragments of equal mass $m$. Then, its total

A body at rest splits into three parts of masses $m, m$ and $4m$, respectively. The two equal masses fly off perpendicular to each other, and each with speed of $v$. The speed of $4m$ will be

A stationary body explodes into two fragments of masses $m_1$ and $m_2$. If momentum of one fragment is $p$, the minimum energy of explosion is 

A two particle system having masses, $M_1$ and $M_2$ are placed in a gravity-free space. If the first particle is shifted towards the centre of mass of the system by a distance $d$, by how much distance should the second particle be shifted so that the centre of mass remains at its initial position?

If the momentum of a body increases by $20\%$, the percentage increase in its kinetic energy is equal to