$A$ bomb at rest explodes into three fragments $X, Y$ and $Z$. Each one of them has the same mass. Which of the following correctly describes the motion of the fragments?

$A$ projectile moving with velocity $v$ in space bursts into $2$ parts with masses in the ratio $1 : 3$. The smaller part becomes stationary. What is the velocity of the other part?

$A$ $6 \,kg$ bomb at rest explodes into three equal pieces $P, Q$ and $R$. If $P$ flies with speed $30 \,m/s$ and $Q$ with speed $40 \,m/s$ making an angle $90^{\circ}$ with the direction of $P$. The angle between the direction of motion of $P$ and $R$ is about (in $^{\circ}$)

The momentum of a system is conserved:

$A$ ball of mass $10 \, kg$ moving with a velocity $10 \sqrt{3} \, m/s$ along the $X$-axis,hits another ball of mass $20 \, kg$ which is at rest. After the collision,the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along the $Y$-axis at a speed of $10 \, m/s$. The second piece starts moving at a speed of $20 \, m/s$ at an angle $\theta$ (in degrees) with respect to the $X$-axis. The configuration of pieces after the collision is shown in the figure. The value of $\theta$ to the nearest integer is:

$A$ bomb of mass $9 \text{ kg}$ explodes into two pieces of mass $3 \text{ kg}$ and $6 \text{ kg}$. The velocity of mass $3 \text{ kg}$ is $16 \text{ m/s}$. The kinetic energy of mass $6 \text{ kg}$ (in joule) is