Question

Eight drops of water, each of radius $2mm$ 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

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 $R=2r\dots \left(i\right)$
Terminal velocity, $v\propto r^2$
$\therefore \frac{v^{\prime }}{v}=\frac{R^2}{r^2}={\left(\frac{2r}{r}\right)}^2=4$ (Using (i))
or $v^{\prime }=4v=4\times 8=32cm{s}^{-1}$