$A$ bullet of mass $0.1\,kg$ is fired with a speed of $100\,m/s$. The mass of the gun is $50\,kg$. The recoil velocity of the gun is ........ $m/s$.

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When both the persons jump simultaneously with $u_{rel}$ with respect to the trolley,then the velocity of the trolley is

$A$ 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 $kg$?

$A$ bomb moving with velocity $(40 \hat{i} + 50 \hat{j} - 25 \hat{k}) \text{ m/s}$ explodes into two pieces of mass ratio $1:4$. After the explosion,the smaller piece moves away with velocity $(200 \hat{i} + 70 \hat{j} + 15 \hat{k}) \text{ m/s}$. The velocity of the larger piece after the explosion is:

$A$ body of mass $14 \ kg$ initially at rest explodes and breaks into three fragments of masses in the ratio $2:2:3$. The two pieces of equal masses fly off perpendicular to each other with a speed of $18 \ m/s$ each. The velocity of the heavier fragment is . . . . . . $m/s$.

$A$ particle of mass $4m$ explodes into three pieces of masses $m, m$ and $2m$. The equal masses move along the $X$-axis and $Y$-axis with velocities $4 \text{ ms}^{-1}$ and $6 \text{ ms}^{-1}$ respectively. The magnitude of the velocity of the heavier mass is