$A$ body of mass $M$ moving with velocity $V$ explodes into two equal parts. If one part comes to rest and the other part moves with velocity $v_{0}$,what would be the value of $v_{0}$?

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. When the man starts moving,then the velocity of the trolley $v_2$ with respect to ground will be

$A$ 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

$A$ 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 $ms^{-1}$)

$A$ 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

Why is the law of conservation of linear momentum a universal and fundamental law?