How do we get to know the concept of mass in Newtonian Mechanics?
Like, from Newton's Second Law of motion we get : $\frac{d\vec P}{dt} = \vec F$ from here, $m\frac{d\vec v}{dt} = F$, defining $\frac{d\vec v}{dt} = \vec a $, we define mass $m = \frac{\vec F}{\vec a}$.
Once again for a constant $\vec F$, we get, $\frac{m_{1}}{m_{2}} = \frac {v_{1}}{v_{2}}$.
Which one (or any other way of defining mass) is correct physical way to define the concept of mass in Newtonian Mechanics?
Place the two masses on a very light glider on an air track, so that they move horizontally with negligible friction. For each mass, pull on the glider with a rubber band, making sure the rubber band is extended to the same length for both masses. Measure the magnitude $a_1$ and $a_2$ of each mass's acceleration. Then the ratio of their masses is \begin{align} \frac{m_1}{m_2} = \frac{a_2}{a_1} \end{align} There is some idealization involved (massless glider, perfectly frictionless and level air track, perfectly elastic rubber band, no uncertainty in the the length of the rubber band or the acceleration), but in principle this is an operational definition of mass.
