I need some help with below. So according to Newton's 2nd law, $a=F/m$, for a given mass, the acceleration depends on mass.
But acceleration due to gravity is independent of mass. There seems some contradiction; I am sure I am missing something, but I can't pin-point what that is.
Acceleration due to gravity remains roughly constant near the surface of the earth. Yes, $a = F/M$, but as mass increases, the force exerted by gravity increases too($ F\ \alpha \ m1m2\over r^2$), keeping $F/M$ or $a$ roughly constant around the surface of the earth
Here's how to intuitively understand that $a=g$.
Take a metal ball having mass 1kg and drop it. Its downward acceleration is $9.8m/s^2$, right? Now take a second ball and drop it. Same thing, right? Now drop both at the same time. Same? Now connect them together (with a tiny drop of weld metal) into a single 2kg mass, and drop them. Do they suddenly slow down? Of course not.
Twice the mass means twice the force - same acceleration.
