Question

Eight drops of water, each of radius $ 2 \,mm $ are falling through air at a terminal velocity of $ 8\, cm \,s^{-1} $ . If they coalesce to form a single drop, then the terminal velocity of combined drop will be

• A. $ 32 \, cm \, s^{-1} $
• B. $ 30\, cm \, s^{-1} $
• C. $ 28\, cm \, s^{-1} $
• D. $ 24\, cm \, s^{-1} $

Answer 1

Answer: (A)

Let the radius of bigger drop is $ R $ and smaller drop is $ r $ then
$ \frac{4}{3} \pi R^{3}=8\times\frac{4}{3}\times\pi r^{3} $
or $ R=2r \ldots\left(i\right) $
Terminal velocity, $ v \propto r^{2} $
$ \therefore \frac{v'}{v}=\frac{R^{2}}{r^{2}}=\left(\frac{2r}{r}\right)^{2}=4 $ (Using (i))
or $ v' =4v=4\times8=32\, cm \, s^{-1} $