$A$ shell of mass $M$ initially at rest suddenly explodes into three fragments. Two of these fragments are of mass $M/4$ each, which move with velocities $3 \text{ m/s}$ and $4 \text{ m/s}$ respectively in mutually perpendicular directions. The magnitude of the velocity of the third fragment is: (in $\text{ m/s}$)

$A$ bomb of mass $30 \, kg$ at rest explodes into two pieces of masses $18 \, kg$ and $12 \, kg$. The velocity of the $18 \, kg$ mass is $6 \, m/s$. The kinetic energy of the other mass is ....... $J$.

$A$ projectile is moving at $20 \, m/s$ at its highest point,where it breaks into two equal parts due to an internal explosion. One part moves vertically up at $30 \, m/s$. Then the other part will move at ............. $m/s$.

$A$ shell,in flight,explodes into four unequal parts. Which of the following is conserved?

$A$ bullet of mass $10\, g$ is fired from a gun of mass $1\, kg$. If the recoil velocity of the gun is $5\, m/s$,the muzzle velocity of the bullet is ........ $m/s$.

Two masses $A$ and $B$ of mass $M$ and $2M$ respectively are connected by a compressed ideal spring. The system is placed on a horizontal frictionless table and given a velocity $u \hat{k}$ in the $z$-direction as shown in the figure. The spring is then released. In the subsequent motion,the line from $B$ to $A$ always points along the $\hat{i}$ unit vector. At some instant of time,mass $B$ has an $x$-component of velocity as $V_x \hat{i}$. The velocity $\vec{V}_A$ of mass $A$ at that instant is: