Question

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

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

Answer 1

The correct option is A $32cm{s}^{-1}$

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 $R=2r$ ....(i)

Terminal velocity,

$v_t=\frac{2}{9}\frac{r^2(\rho -\sigma )g}{\eta }$

$v_t\propto r^2$

$\frac{v^{\prime }}{v}=\frac{R^2}{r^2}={\left(\frac{2r}{r}\right)}^2=4$ (Using (i))

or $v^{\prime }=4v=4\times 8=32cm{s}^{-1}$