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

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 $v=\frac{2r^2(\rho -\sigma )}{9\eta }$ $\Rightarrow$ $v\propto r^2$ $\Rightarrow$ $\frac{v_1}{v_2}={\left(\frac{r}{R}\right)}^2={\left(\frac{1}{4}\right)}^2=\frac{1}{16}$ $\therefore$ $v_{12}=16v_1=16\times 1.5=24m{s}^{-1}$