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

An object of mass $2 \,kg$ at rest at origin starts moving under the action of a force $\vec{F}=\left(3 t^2 \hat{i}+4 \hat{j}\right) N$ The velocity of the object at $t=2 \,s$ will be ............. $m / s$

Two spheres $A$ and $B$ of masses $m_1$ and $m_2$ respectively collide. $A$ is at rest initially and $B$ is moving with velocity $v$ along $x-$ axis. After collision $B$  has a $\frac {v}{2}$ velocity in a direction perpendicular to the original direction. The mass $A$ moves after collision in the direction

A body of mass $M$ at rest explodes into three pieces, in the ratio of masses $1: 1: 2$. Two smaller pieces fly off perpendicular to each other with velocities of $30 \,ms ^{-1}$ and $40 \,ms ^{-1}$ respectively. The velocity of the third piece will be ............... $\,ms ^{-1}$

A machine gun of mass $10\,kg$ fires $20\,g$ bullets at the rate of $180$ bullets per minute with a speed of $100\,m s ^{-1}$ each. The recoil velocity of the gun is $.............\,m/s$