Question

Two drops of small radius are falling in air with constant velocity $5cm{s}^{-1}$. If they coalesce, then the terminal velocity will be

• A. $10cm{s}^{-1}$
• B. $2.5cm{s}^{-1}$
• C. $5\times \sqrt[3]{34}cm{s}^{-1}$
• D. $5.\sqrt{2}cm{s}^{-1}$

Answer 1

The correct option is C $5\times \sqrt[3]{34}cm{s}^{-1}$

Let the radius of smaller drops =r $r^3=V$
radius of larger coslesce drop= $2^{1/3}r$
$V$ of smaller drops =$=\frac{2g(T-s)r^2}{9\eta }=5$ ----------(1)
$V$ of larger drops= $=\frac{2g(T-s)r^2}{9\eta }{2}^{2/3}$[from(1)]
$=5\times 2^{2/3}cm/s$
$=5\times \sqrt[3]{34}cm/s$