$A$ bullet of mass $m$ is fired from a rifle of mass $M$. If $v$ is the velocity of the bullet,the velocity acquired by the rifle is:

An object flying in air with velocity $(20 \hat{i}+25 \hat{j}-12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio $1:5$. The smaller mass flies off with a velocity $(100 \hat{i}+35 \hat{j}+8 \hat{k})$. The velocity of the larger piece will be:

$A$ spacecraft of mass $M$ moving with velocity $v$ suddenly breaks into two pieces of equal mass $m$. After the explosion,one of the masses $m$ becomes stationary. What is the velocity of the other part of the craft?

$A$ ball of mass $m = 60 \text{ g}$ is shot with speed $v_0 = 22 \text{ m/s}$ into the barrel of a spring gun of mass $M = 240 \text{ g}$,which is initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. The speed of the spring gun after the ball stops relative to the barrel is:

$A$ trolley of mass $1000\, kg$ is moving with a velocity of $50\, km/h$. If a mass of $250\, kg$ is added to it,what will be the new velocity in $km/h$?

$A$ stationary body explodes into two parts of masses $M_{1}$ and $M_{2}$. They move in opposite directions with velocities $v_{1}$ and $v_{2}$. The ratio of their kinetic energies is