Particle $A$ of mass $m _{1}$ moving with velocity $(\sqrt{3} \hat{i}+\hat{j})\, ms ^{-1}$ collides with another particle $B$ of mass $m _{2}$ which is at rest initially. Let $\overrightarrow{ V }_{1}$ and $\overrightarrow{ V }_{2}$ be the velocities of particles $A$ and $B$ after collision respectively. If $m _{1}=2\, m _{2}$ and after collision $\overrightarrow{ V }_{1}=(\hat{ i }+\sqrt{3} \hat{ j })\, ms ^{-1},$ the angle between $\overrightarrow{ V }_{1}$ and $\overrightarrow{ V }_{2}$ is$......^o$

A hemisphere of radius $R$ and of mass $4m$ is free to slide with its base on a smooth horizontal table. A particle of mass $m$ is placed on the top of the hemisphere. The angular velocity of the particle relative to hemisphere at an angular displacement $\theta $ when velocity of hemisphere $v$ is

A bomb is projected with $200\,m/s$ at an angle $60^o$ with horizontal. At the highest point, it explodes into three particles of equal masses. One goes vertically upward with velocity $100\,m/sec,$ second particle goes vertically downward with the same velocity as the first. Then what is the velocity of the third one

Two skaters $A$ and $B$ of weights in the ratio $5 : 7$ start facing each other $6\,metres$ apart on a horizontal smooth surface. They pull on a rope stretched between them. How far has each moved when they meet?

An object of mass $3\,m$ splits into three equal fragments. Two fragments have velocities $v\hat j$ and $v\hat i$. The velocity of the third fragment is

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 $.....\,Ns$