Let, M = mass of nucleus at rest . m1 and m2 are masses of two smaller nuclei. v1 and v2 are the velocities of respective masses
Now, According to the law of conservation of momentum,
Initial momentum before disintegration = final momentum after disintegration
As masses and cannot be negative, and having opposite signs and so the two smaller nuclei move in opposite directions.

Since, density
= mass / volume ;
and SI unit of mass is kg and that of volume is
using these SI units the unit of density is derived through dimensional analysis :
density = mass / volume
= kg / m3
or, = kg m-3