$A$ bomb of mass $3m \text{ kg}$ explodes into two pieces of mass $m \text{ kg}$ and $2m \text{ kg}$. If the velocity of the $m \text{ kg}$ mass is $16 \text{ m/s}$,the total kinetic energy released in the explosion is ................. $m \text{ J}$.

In a gravity-free space,a man of mass $M$ standing at a height $h$ above the floor,throws a ball of mass $m$ straight down with a speed $u$. When the ball reaches the floor,the distance of the man above the floor will be

$A$ spacecraft of mass $M$ is moving in space with a velocity $v$. It explodes and breaks into two pieces. After the explosion,a piece of mass $m$ comes to rest. The velocity of the other piece is ......

$A$ 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

An object flying in air with velocity $(20 \hat{i}+25 \hat{j}-12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio $1:5$. The smaller mass flies off with a velocity $(100 \hat{i}+35 \hat{j}+8 \hat{k})$. The velocity of the larger piece will be:

$A$ ball is projected at $60^{\circ}$ from the horizontal at $200 \, m/s$. At the maximum height during its flight,it explodes into $3$ equal fragments. Out of these,one part travels at $100 \, m/s$ vertically up while another travels at $100 \, m/s$ vertically down. What will be the speed of the third part just after the explosion?