A man fires a bullet of mass $200 \,g$ at a speed of $5 \,m/s$. The gun is of one $kg$ mass. by what velocity the gun rebounds backwards …….. $m/s$

A bullet mass $10\, gm$ is fired from a gun of mass $1\,kg$. If the recoil velocity is $5\, m/s$, the velocity of the muzzle is …….. $m/s$

A bullet $10\,g$ leaves the barrel of gun with a velocity of $600\,m / s$. If the barrel of gun is $50\,cm$ long and mass of gun is $3\,kg$, then value of impulse supplied to the gun will be $…..\,Ns$

A shell at rest at the origin explodes into three fragments of masses $1\ kg$ , $2\ kg$ and $m\ kg$ . The $1\ kg$ and $2\ kg$ pieces fly off with speeds of $5\ ms^{-1}$ along $x-axis$ and $6\ ms^{-1}$ along $y-axis$ respectively. If the $m\, kg$ piece flies off with a speed of $6.5\ ms^{-1}$ , the total mass of the shell must be    ……… $kg$

Two identical billiard balls strike a rigid wall with the same speed but at different angles, and get reflected without any change in speed, as shown in Figure. What is

$(i)$ the direction of the force on the wall due to each ball?

$(ii)$ the ratio of the magnitudes of impulses imparted to the balls by the wall ?