An isolated rail car originally moving with speed $v_0$ on a straight, frictionles, level track contains a large amount of sand. $A$ release valve on the bottom of the car malfunctions, and sand begins to pour out straight down relative to the rail car. Is momentum conserved in this process?

A bullet $10\,g$ leaves the barrel of gun with a velocity of $600\,m / s$. If the barrel of gun is $50\,cm$ long and mass of gun is $3\,kg$, then value of impulse supplied to the gun will be $…..\,Ns$

Three particles of masses $10\;g, 20\;g$ and $40\;g$ are moving with velocities $10\widehat i,10\widehat j$ and  $10\widehat k\;m/s$ respectively. If due to some mutual interaction, the first particle comes to  rest and the velocity of second particle becomes $\left( {3\widehat i + 4\widehat j\,\,} \right)\, m/s$, then the velocity of third particle is

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1\, kg$ moves with a speed of $12 \,m s^{-1}$ and the second part of mass $2\, kg$ moves with $8 \,m s^{-1}$ speed. If the third part files off with $4 \,m s^{-1}$ speed, then its mass is ……… $kg$