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Suppose Galileo dropped a one-kilogram ball of cotton and one-kilogram ball of iron from the top of the Leaning Tower of Pisa, then which one will reach the ground first? Assume that the cotton ball is tightly wadded up and that initially the bottoms of the cotton ball and iron ball are at the same horizontal level. source

The answer to this question apparently is the iron ball, but I don't see any reason why that'd be, considering that they have equal masses! Does density affect the rate at which an object falls?

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    $\begingroup$ Not density so much as surface area which causes drag. Presumably, the Leaning Tower of Pisa is not in a vacuum chamber. $\endgroup$
    – DKNguyen
    Apr 23, 2021 at 3:36

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The cotton would have greater air resistance so it would fall slower. However, neglecting air resistance, all masses in the same gravitational field fall at the same rate. Near Earth's surface objects fall at about 9.8 meters per second squared, neglecting air resistance. Here is an interesting clip of a feather and a hammer being dropped on the Moon where there is negligible air resistance; https://www.youtube.com/watch?v=Oo8TaPVsn9Y

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  • $\begingroup$ So does the cotton ball experience a greater air resistance because it's (likely) bigger than the iron one? $\endgroup$
    – Shane
    Apr 23, 2021 at 5:50
  • $\begingroup$ it experiences same air resistance (air resistance refers to the retarding FORCE ) but the effect of that resistance i.e the deceleration is more for cotton than for iron since iron is heavier than cotton $\endgroup$
    – Möbius
    Apr 23, 2021 at 6:10
  • $\begingroup$ But the iron & the cotton balls used here are of the same mass... $\endgroup$
    – Shane
    Apr 23, 2021 at 12:10
  • $\begingroup$ The kilo of cotton will likely be larger than the kilo of iron so it will have greater air drag. Think of a feather and a BB, they may weigh about the same but they do not have the same amount of air drag. $\endgroup$
    – Adrian Howard
    Apr 23, 2021 at 19:20
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It depends on air resistance. If you have two objects with different masses then the object with greater mass falls faster. But here , since the masses are equal , now the fall rate depends on- surface area and density of the fluid.

If an object has more surface area, it has more volume which means it has less density. So more the surface area, more the drag coefficient which means object with less density will fall faster

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  • $\begingroup$ "If you have two objects with different masses then the object with greater mass falls faster." Not necessarily. A small stone might fall much faster than a man in a parachute. $\endgroup$
    – Math Keeps Me Busy
    Apr 23, 2021 at 3:47
  • $\begingroup$ When a 1 kilo iron ball and a 10 kilo iron ball fall, the larger mass will not necessarily fall faster. $\endgroup$
    – Adrian Howard
    Apr 23, 2021 at 4:27
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When any object falls through a fluid like air it experiences viscous force.This force produces a deceleration that can be expressed as :$$ \vec F = m \vec a$$$$\vec a = \frac{\vec F }{m}$$ So magnitude of deceleration due to Viscous force is :$$|a| =\frac {|F_{viscous}|}{m}$$ The viscous force depends only on mass and surface area so the viscous forces experienced by cotton ball and iron ball of same size are equal.

However in case of cotton the quantity, $$\frac {|F_{viscous}|}{m}$$ is large since mass is small and so the deceleration is also large .

But for iron the same quantity,$$\frac {|F_{viscous}|}{m}$$ is small since mass is large so the deceleration is also small.

Now both cotton and iron have same acceleration due to gravity downward but due to more deceleration in case of cotton the cotton ball takes more time reach the ground than the iron ball that takes less time as it experiences less deceleration.

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