Question

A body explodes in mid-air. Does its momentum remain conserved?

Answer 1

During explosion, the net force acting on the system (fragments or particles of the body) is the weight of the system, that is $mg$, where $m$ is the mass of the body. In this case we see that the change of momentum of the centre of the system (exploded particles) due to gravitational force (Weight mg) is negligible during very short time of explosion
$\Rightarrow \Delta p={\int }_0^{\Lambda t}{F}_{ext}dt\Rightarrow \Delta p=F_{ext}\Delta t;F_{ext}=mg$
Since $\Delta t\to 0,\Delta p\to 0$
The momentum of the system before and after the impact remains practically equal. As the time interval is very small there is no (Significant) appreciable change in the momentum of the centre of mass of the system, due to the external gravitational force.