Conservation of Momentum

Linear momentum of a system is conserved only if the net external force acting on the system is zero.

A $10 \mathrm{kg}$ ball moving at $20 \mathrm{m}/\mathrm{s}$ strikes a second ball at rest. After the collision the $10 \mathrm{kg}$ ball is moving with a velocity of $10 \mathrm{m}/\mathrm{s}$ and the second ball is moving with a velocity of $5 \mathrm{m}/\mathrm{s}$. Mass of the second ball in kilogram is 

A bullet of mass $5 \mathrm{g}$ is fired from a pistol of mass $1.5 \mathrm{kg}$. The recoil velocity of pistol is $1.5 \mathrm{m}/\mathrm{s}$. The velocity of bullet fired from gun in $\mathrm{m}/\mathrm{s}$ is 

A bag of sand of mass $M$ is hanging from a rope. A bullet of mass $\frac{M}{2}$ is fired at it with a velocity $u \mathrm{m}/\mathrm{s}$. The bullet gets embedded into the bag. What is the velocity of the bag after the bullet gets embedded into it?
 

A thin ring of mass $2 \mathrm{kg}$ and radius $0.5 \mathrm{m}$ is rolling without slipping on a horizontal plane with velocity $1 \mathrm{m} {\mathrm{s}}^{-1}$. A small ball of mass $0.1 \mathrm{kg}$, moving with velocity $20 \mathrm{m} {\mathrm{s}}^{-1}$ in the opposite direction, hits the ring at a height of $0.75 \mathrm{m}$ and goes vertically up with velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$. Immediately after the collision