A ball will a speed of $9\, m / s$ collides with another identical ball at rest. After the collision, the direction of each ball makes an angle of $30^{\circ}$ with the original direction. The ratio of velocities of the balls after collision is $x : y$ where $x$ is........

A bullet of mass $40 \,g$ is fired from a gun of mass $10 \,kg$. If velocity of bullet is $400 \,m / s$, then the recoil velocity of the gun will be ..........

A jet engine works on the principle of

A body of mass $M$ at rest explodes into three pieces, two of which of mass $M/4$ each are thrown off in perpendicular directions with velocities of $3\, m/s$ and $4\, m/s$ respectively. The third piece will be thrown off with a velocity of .......... $m/s$

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 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 ........ $m/sec$