$A$ 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 .......... $kg$.

$A$ man of $50 \,kg$ is standing at one end of a boat of length $25 \,m$ and mass $200 \,kg$. If he starts running and when he reaches the other end, he has a velocity $2 \,ms^{-1}$ with respect to the boat. The final velocity of the boat is : (in $ms^{-1}$ )

$A$ 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

$A$ bullet is fired from a rifle. If the rifle recoils freely,then the kinetic energy of the rifle is

$A$ body at rest breaks into three fragments. Two fragments of equal mass fly off perpendicular to each other with a speed of $30 \; m/s$. The mass of the third fragment is three times that of the other two fragments. What will be the direction and magnitude of the velocity of the third fragment immediately after the explosion?

$A$ man of mass $m_1$ is standing on a platform of mass $m_2$ kept on a smooth horizontal surface. If the man starts moving on the platform with a velocity $v$ relative to the platform,then the recoil velocity of the platform is: