$A$ 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 $4 M$ which is initially at rest explodes into three pieces of masses $M, M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 \ m s^{-1}$ and $6 \ m s^{-1}$ respectively. The magnitude of the velocity of the heavier mass is

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

$A$ shell of mass $200\, g$ is ejected from a gun of mass $4\, kg$ by an explosion that generates $1.05\, kJ$ of energy. The initial velocity of the shell is .............. $m/s$.

$A$ bomb of mass $9 \,kg$ explodes into two pieces of masses $3 \,kg$ and $6 \,kg$. The velocity of mass $3 \,kg$ is $16 \,m/s$. The kinetic energy of mass $6 \,kg$ in joule is

Two balls in free space are colliding with each other. Which of the following statements regarding linear momentum conservation of the system is true?