$A$ shell of mass $m$ moving with velocity $v$ suddenly breaks into two pieces. The part having mass $\frac{m}{5}$ remains stationary. The velocity of the other part will be

Two blocks $A$ and $B$ of masses $1\, kg$ and $2\, kg$ are connected together by a spring and are resting on a horizontal surface. The blocks are pulled apart so as to stretch the spring and then released. The ratio of $K.E.$ of block $A$ to the $K.E.$ of block $B$ is:

$A$ bomb of mass $10\, kg$ explodes into two pieces of masses $4\, kg$ and $6\, kg$. If the kinetic energy of the $4\, kg$ piece is $200\, J$,find the kinetic energy of the $6\, kg$ piece.

$A$ 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

$A$ man of $50 \,kg$ is standing at one end of a boat of length $25 \,m$ and mass $200 \,kg$. If he starts running and when he reaches the other end, he has a velocity $2 \,ms^{-1}$ with respect to the boat. The final velocity of the boat is: (in $ms^{-1}$)

$A$ spacecraft of mass $M$ is moving with velocity $V$ and suddenly explodes into two pieces. $A$ part of it of mass $m$ comes to rest. The velocity of the other part will be: