Question

Sixty four spherical rain drops of equal size are falling vertically through air with a terminal velocity $ 1.5\,\text{m}{{\text{s}}^{-1}}. $ If these drops coalesce to form a big spherical drop, then terminal velocity of big drop is :

• A. $ 8\,m{{s}^{-1}} $
• B. $ 16\,m{{s}^{-1}} $
• C. $ 24\,m{{s}^{-1}} $
• D. $ 32\,m{{s}^{-1}} $

Answer 1

Answer: (C)

Volume of big drop $ =64\times $ volume of a smalldrop $ \Rightarrow $ $ \frac{4}{3}\pi {{R}^{3}}=64\times \frac{4}{3}\pi {{r}^{3}} $ $ \Rightarrow $ $ R=4r $ The terminal velocity of spherical rain drop $ v=\frac{2{{r}^{2}}(\rho -\sigma )}{9\eta } $ $ \Rightarrow $ $ v\propto {{r}^{2}} $ $ \Rightarrow $ $ \frac{{{v}_{1}}}{{{v}_{2}}}={{\left( \frac{r}{R} \right)}^{2}}={{\left( \frac{1}{4} \right)}^{2}}=\frac{1}{16} $ $ \therefore $ $ {{v}_{12}}=16\,{{v}_{1}}=16\times 1.5=24\,m{{s}^{-1}} $