I did an experiment in which I dropped three different sized spherical beads (4mm, 6mm, and 11mm diameter) with the same densities through a viscous liquid (a water-detergent solution). They all fell the same distance, but the biggest one fell a full ten seconds faster than the smallest one. What could be the explanation for this? I would have thought the opposite due to friction and the fact that gravity affects everything the same. Why did the biggest one fall fastest?
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$\begingroup$ The first results will already answer your question: google.com/… $\endgroup$– stafusaCommented Sep 16, 2017 at 15:51
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$\begingroup$ @stafusa ironically, first result now goes to this question :) $\endgroup$– LopeCommented Sep 17, 2017 at 12:23
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$\begingroup$ @Lope, see, I told the search answered the question ;-P More seriously, it's interesting how it became the first google result in less than 24h. $\endgroup$– stafusaCommented Sep 17, 2017 at 12:29
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You have pointed out the difference between rain drops (large radius) and mist drops (small radius) which fall much slower.
When terminal velocity $v$ is reached the viscous drag on a sphere of density $\rho$ and radius $r$, $6\pi r v \eta$, is equal to the apparent weight of the sphere $\frac 43\pi r^3 (\rho -\sigma)g$ where $\sigma$ is the density of the fluid and $\eta$ its viscosity.
From this you get that $v \propto r^2$.
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$\begingroup$ Rain drops won't be in the Stokes drag, but in the Newton drag regime (inertial term important). $\endgroup$ Commented Sep 16, 2017 at 19:49
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2$\begingroup$ @VladimirF I agree but I thought that the analogy was a reasonable one to make to illustrate what was observed in a viscous liquid. $\endgroup$– FarcherCommented Sep 16, 2017 at 20:07