$12 \,kg$ bomb at rest explodes into two pieces of $4 \,kg$ and $8 \,kg$. If the momentum of the $4 \,kg$ piece is $20 \,Ns$, what is the kinetic energy of the $8 \,kg$ piece (in $\,J$)?

$A$ ball of mass $200\,g$ rests on a vertical post of height $20\,m$. $A$ bullet of mass $10\,g$,travelling in a horizontal direction,hits the centre of the ball. After the collision,both travel independently. The ball hits the ground at a distance of $30\,m$ and the bullet at a distance of $120\,m$ from the foot of the post. The value of the initial velocity of the bullet will be $............m/s$ (if $g = 10\,m/s^2$).

$A$ cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy $E_1$ and the kinetic energy of the second part is $E_2$. The relation between $E_1$ and $E_2$ is:

$A$ shell of mass $0.020 \; kg$ is fired by a gun of mass $100 \; kg$. If the muzzle speed of the shell is $80 \; m s^{-1}$,what is the recoil speed in $m/s$ of the gun?

$A$ 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 ......

$A$ 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 ............. $J$.