Newton's 2nd Law says $\vec{F}= \frac{d\vec{p}}{dt}$ . 

In a constant mass system this becomes $\vec{F}=m\vec{a}$, which many answers give experiments to prove. Answers to why $F=ma$ can be found [here](https://physics.stackexchange.com/questions/172848/why-does-f-ma-is-there-a-straightforward-reason).

However, in a [variable mass sytem](https://en.wikipedia.org/wiki/Variable-mass_system#Derivation) Newton's 2nd law still applies and it becomes ${\mathbf  {F}}_{{{\mathrm  {ext}}}}+{\mathbf  {v}}_{{{\mathrm  {rel}}}}{\frac  {{\mathrm  {d}}m}{{\mathrm  {d}}t}}=m{{\mathrm  {d}}{\mathbf  v} \over {\mathrm  {d}}t}$
. What experimental evidence is there for this (both that Newton's law will apply and/or that this equation is correct)?