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 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........

You are on a frictionless horizontal plane. How can you get off if no horizontal force is exerted by pushing against the surface

A rifle man, who together with his rifle has a mass of $100\,kg$, stands on a smooth surface and fires $10$ shots horizontally. Each bullet has a mass $10\,g$ and a muzzle velocity of $800\,ms ^{-1}$. The velocity which the rifle man attains after firing $10$ shots is $..........\,ms^{-1}$

If final momentum is equal to initial momentum of the system then

A ball is projected at $60^o$ from horizontal at $200\, m/s$. At maximum height during its  flight it explodes into $3$ equal fragments. Out of them one part travel at $100\, m/s$  vertically up while other at $100\, m/s$ vertically down, then third part will have  speed just after explosion :-