An explosion blows a stationary rock into three parts. Two parts of masses $1 \,kg$ and $2 \,kg$ move at right angles to one another with velocities $12 \,ms^{-1}$ and $8 \,ms^{-1}$, respectively. If the velocity of the third part is $4 \,ms^{-1}$, the mass of the rock is (in $\,kg$)

$A$ ball of mass $m = 60 \text{ g}$ is shot with speed $v_0 = 22 \text{ m/s}$ into the barrel of a spring gun of mass $M = 240 \text{ g}$,which is initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. The speed of the spring gun after the ball stops relative to the barrel is:

$A$ bullet of mass $5 \,g$ is shot from a gun of mass $5 \,kg$. The muzzle velocity of the bullet is $500 \,m/s$. The recoil velocity of the gun is ........... $m/s$.

When two balls at the same temperature collide,which of the following quantities is conserved?

$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M, M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 \ m s^{-1}$ and $6 \ m s^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

$A$ system of $N$ particles is free from any external forces. Which of the following is true for the magnitude of the total momentum of the system?