$A$ stationary body explodes into two parts of masses $M_1$ and $M_2$. They move in opposite directions with velocities $V_1$ and $V_2$. The ratio of their kinetic energies is

An object flying in air with velocity $(20 \hat{i}+25 \hat{j}-12 \hat{k})$ suddenly breaks into two pieces whose masses are in the ratio $1:5$. The smaller mass flies off with a velocity $(100 \hat{i}+35 \hat{j}+8 \hat{k})$. The velocity of the larger piece will be:

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:

$A$ shell,in flight,explodes into four unequal parts. Which of the following is conserved?

$A$ projectile of mass $3m$ is moving at $40\, m/s$ at its highest point,where it breaks into two parts $m$ and $2m$. Mass $2m$ moves vertically up at $25\, m/s$. The other part will move at a speed of .................... $m/s$.

From a stationary tank of mass $125000 \ lb$,a small shell of mass $25 \ lb$ is fired with a muzzle velocity of $1000 \ ft/sec$. The tank recoils with a velocity of ............ $ft/sec$.