$A$ body initially at rest breaks up into two pieces of masses $2 M$ and $3 M$ respectively,together having a total kinetic energy $E$. The piece of mass $2 M$,after breaking up,has a kinetic energy:

$A$ spacecraft of mass $M$ moves with velocity $V$ in free space. It explodes and breaks into two pieces. If after the explosion,a piece of mass $m$ comes to rest,what will be the velocity of the other piece of the spacecraft?

$A$ stationary particle explodes into two particles of masses $x$ and $y$,which move in opposite directions with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $(E_1: E_2)$ is

$A$ 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?

$A$ projectile is fired with velocity $u$ at an angle $\theta$ with the horizontal. At the highest point of its trajectory,it splits into three segments of masses $m, m$,and $2m$. The first part falls vertically downward with zero initial velocity,and the second part returns via the same path to the point of projection. The velocity of the third part of mass $2m$ just after the explosion will be:

$A$ body at rest breaks up into $3$ parts. If $2$ parts having equal masses $m$ fly off perpendicularly to each other,each with a velocity of $12 \, m/s$,then the velocity of the third part,which has $3$ times the mass of each part,is: