$A$ gun fires a bullet of mass $50 \ g$ with a velocity of $30 \ m \ s^{-1}$. Due to this,the gun recoils with a velocity of $1 \ m \ s^{-1}$. What is the mass of the gun in $kg$?

$A$ 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:

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/4$ remains stationary. The velocity of the other shell will be

$A$ man is standing at the centre of a frictionless pond of ice. How can he get himself to the shore?

State the law of conservation of total linear momentum for a system of particles.

$A$ spaceship of speed $v_0$ travelling along $+y$ axis suddenly shoots out one-fourth of its part with speed $2v_0$ along $+x$ axis. The $xy$ axes are fixed with respect to the ground. The velocity of the remaining part is: