$A$ bullet of mass $m$ is fired from a gun of mass $M$. If the velocity of the bullet is $v$,what will be the recoil velocity of the gun?

$A$ gun fires a bullet of mass $50 \, g$ with a velocity of $30 \, m/s$. Because of this,the gun is pushed back with a velocity of $1 \, m/s$. The mass of the gun is .......... $kg$.

$A$ bullet of mass $50 \, g$ is fired from a $5 \, kg$ gun with a velocity of $1 \, km/s$. The speed of recoil of the gun is .......... $m/s$.

$A$ body at rest breaks up into $3$ parts. If $2$ parts having equal masses $m$ fly off perpendicularly to each other,each with a velocity of $12 \, m/s$,then the velocity of the third part,which has $3$ times the mass of each part,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 $km/h$?

$A$ cannon shell fired breaks into two equal parts at its highest point. If one part retraces its path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$,then