$A$ stationary particle explodes into two particles of masses $x$ and $y$,which move in opposite directions with velocities $v_1$ and $v_2$. The ratio of their kinetic energies $(E_1: E_2)$ is

$A$ bomb of mass $12 \ kg$ initially at rest explodes into two fragments with a mass ratio of $1:3$. The kinetic energy of the smaller fragment is $216 \ J$. What is the momentum of the larger (heavier) fragment in $kg \cdot m/s$?

$A$ bomb of mass $1 \,kg$ initially at rest,explodes and breaks into three fragments of masses in the ratio $1: 1: 3$. The two pieces of equal mass fly off perpendicular to each other with a speed $15 \,m / s$ each. The speed of the heavier fragment is ........... $m / s$.

$A$ bomb of mass $16 \ kg$ at rest explodes into two pieces of masses $4 \ kg$ and $12 \ kg.$ The velocity of the $12 \ kg$ mass is $4 \ m s^{-1}.$ The kinetic energy of the other mass is .............. $J$.

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When both the persons jump simultaneously with $u_{rel}$ with respect to the trolley,then the velocity of the trolley is

$A$ 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: