$A$ bullet of mass $0.1\,kg$ is fired with a speed of $100\,m/s$. The mass of the gun is $50\,kg$. The recoil velocity of the gun is ........ $m/s$.

$A$ shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2:2:1$. If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$,the speed of the third (lighter) fragment is:

State and explain the law of conservation of momentum for a system of particles.

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be

$A$ vessel at rest explodes into three pieces. Two pieces having equal masses $m$ fly off perpendicular to one another with the same velocity $30 \, m/s$. The third piece has three times the mass of each of the other pieces. The magnitude and direction of the velocity of the third piece will be:

Two balls in free space are colliding with each other. Which of the following statements regarding linear momentum conservation of the system is true?