A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass $${1 \over 3}$$ $$M$$ and a body $$C$$ of mass $${2 \over 3}$$ $$M.$$ The center of mass of bodies $$B$$ and $$C$$ taken together shifts compared to that of bodies $$B$$ and $$C$$ taken together shifts compared to that of body $$A$$ towards

A machine gun fires a bullet of mass $$40$$ $$g$$ with a velocity $$1200m{s^{ - 1}}.$$ The man holding it can exert a maximum force of $$144$$ $$N$$ on the gun. How many bullets can he fire per second at the most?

Consider the following two statements :

$$A.$$ Linear momentum of a system of particles is zero

$$B.$$ Kinetic energy of a system of particles is zero.

then

Two identical particles move towards each other with velocity $$2v$$ and $$v$$ respectively. The velocity of center of mass is