$A$ bomb of $12 \, kg$ explodes into two pieces of masses $4 \, kg$ and $8 \, kg$. The velocity of the $8 \, kg$ mass is $6 \, m/s$. The kinetic energy of the other mass is ............. $J$.

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

$A$ mass of $1 \; kg$ is thrown up with a velocity of $100 \; m/s$. After $5 \; s$,it explodes into two parts. One part of mass $400 \; g$ comes down with a velocity of $25 \; m/s$. Calculate the velocity of the other part.

$A$ 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:

At a certain height,a body at rest explodes into two equal fragments with one fragment receiving a horizontal velocity of $10\sqrt{3} \text{ m/s}$. The horizontal distance between the two fragments,when their displacement vectors are inclined at $60^{\circ}$ relative to each other,is (take $g = 10 \text{ m/s}^2$):

$A$ body,whose momentum is constant,must have constant