Under the influence of mutual internal forces,which of the following is true for a system?

$A$ shell of mass $20 \,kg$ at rest explodes into two fragments whose masses are in the ratio $2 : 3$. The smaller fragment moves with a velocity of $6 \,ms^{-1}$. The kinetic energy of the larger fragment is (in $\,J$)

$A$ body of mass $5 \ kg$ initially at rest explodes into three fragments. The ratio of the masses of the three fragments is $1 : 1 : 3$. The two fragments of equal mass move in mutually perpendicular directions with a velocity of $21 \ m/s$. What is the velocity of the heaviest fragment in $m/s$?

$A$ bomb at rest explodes into three parts of equal mass. If the momentum of two parts are $-2 p \hat{i}$ and $p \hat{j}$,find the magnitude of momentum of the third part.

An artillery piece of mass $M_1$ fires a shell of mass $M_2$ horizontally. Instantaneously after the firing,the ratio of kinetic energy of the artillery and that of the shell is:

$A$ bomb at rest explodes into three equal fragments. Two of the fragments move at right angles to each other with velocities of $9 \ m s^{-1}$ and $12 \ m s^{-1}$. The magnitude of the velocity of the third fragment is ....... $m s^{-1}$.