$A$ bomb of mass $12\,kg$ at rest explodes into two fragments of masses in the ratio $1 : 3$. The $K.E.$ of the smaller fragment is $216\,J$. The momentum of the heavier fragment is (in $kg\cdot m/s$):

$A$ 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 ....... $m s^{-1}$.

$A$ trolley of mass $200\; kg$ moves with a uniform speed of $36\; km/h$ on a frictionless track. $A$ child of mass $20\; kg$ runs on the trolley from one end to the other ($10\; m$ away) with a speed of $4\; m/s$ relative to the trolley in a direction opposite to its motion,and jumps out of the trolley. What is the final speed of the trolley? How much has the trolley moved from the time the child begins to run?

$A$ shell in free space initially at rest explodes into two pieces,$A$ and $B$,which then move in opposite directions. Piece $A$ has less mass than piece $B$. Ignore all external forces. Identify the correct statement.

$A$ 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 $m/s$?

$A$ 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 $\,J$)