I have a doubt about this question:
Two bodies of masses $M$ and $m$ are allowed to fall from the same height. If the air resistance be the same for each of the bodies, will the two bodies reach the Earth simultaneously? Justify.
The answer given is not that both reach at same time. I fail to understand why?
According to the equation by Galileo:
$a=\frac{F}{m}=\frac{GM_\oplus}{R^2}$
where $M_\oplus$ is the mass of the Earth, $R$ is the radius of the Earth, and $G$ is Newton's gravitational constant.
So the acceleration is independent of the mass. So in this question both the bodies should fall at the same time.
Is it that due to air resistance the force on $M$ will be more or something?
Best Answer
I suspect it's all in what they meant by "air resistance is the same ." For example, if both bodies are the same size and shape, the equation for air resistance as a func of velocity is the same, but the greater mass will be less affected by this equal force magnitude. Air resistance being "same" is not the same thing as being "neglectable" or "zero."