$A$ bomb of mass $12 \ kg$ initially at rest explodes into two fragments with a mass ratio of $1:3$. The kinetic energy of the smaller fragment is $216 \ J$. What is the momentum of the larger (heavier) fragment in $kg \cdot m/s$?

$A$ man of mass $100\,kg$ is standing on a platform of mass $200\,kg$ which is kept on a smooth ice surface. If the man starts moving on the platform with a speed $30\,m/s$ relative to the platform,then calculate with what velocity relative to the ice the platform will recoil.

$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into $2$ pieces. The part having mass $m/3$ remains stationary. The velocity of the other part will be

An isolated rail car of mass $M$ is moving along a straight,frictionless track at an initial speed $v_0$. The car is passing under a bridge when a crate filled with $N$ bowling balls,each of mass $m$,is dropped from the bridge into the bed of the rail car. The crate splits open and the bowling balls bounce around inside the rail car,but none of them fall out. Is the momentum of the rail car $+$ bowling balls system conserved in this collision?

If the resultant of all the external forces acting on a system of particles is zero,then from an inertial frame,one can surely say that

$A$ spacecraft of mass $M$ moves with velocity $V$ in free space at first,then it explodes breaking into two pieces. If after explosion a piece of mass $m$ comes to rest,the other piece of spacecraft will have a velocity