$A$ 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?

$A$ shell is fired from a cannon with a velocity $V$ at an angle $\theta$ with the horizontal direction. At the highest point in its path,it explodes into two pieces of equal masses. One of the pieces comes to rest. The speed of the other piece immediately after the explosion is

$A$ bomb of mass $10\, kg$ explodes into two pieces of masses $4\, kg$ and $6\, kg$. If the kinetic energy of the $4\, kg$ piece is $200\, J$,find the kinetic energy of the $6\, kg$ piece.

Three masses $m$,$2m$,and $3m$ are moving in the $x-y$ plane with speeds $3u$,$2u$,and $u$ respectively,as shown in the figure. The three masses collide at the same point $P$ and stick together. The velocity of the resulting mass will be

$A$ particle of mass $m$ travelling along the $x$-axis with speed $v_0$ shoots out $1/3$ of its mass with a speed $2v_0$ along the $y$-axis. The velocity of the remaining piece is:

Two blocks $A$ and $B$ of masses $1\, kg$ and $2\, kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.$ of block $A$ to the $K.E.$ of block $B$ is: