Question

A drop of liquid having radius 2mm has a terminal velocity 20cms${}^{-1}$, the terminal velocity of a drop 1mm radius will be:

• A. 40 cms${}^{-1}$
• B. 20 cms${}^{-1}$
• C. 10 cms${}^{-1}$
• D. 5 cms${}^{-1}$

Answer 1

Answer: (D)

5 cms${}^{-1}$

Let velocity of 1mm radius drop=V
$=\frac{2g(\sigma -T)r^2}{9\eta }=\frac{2g(\sigma -T)}{9\eta }{1}^2$-----------(1)
Velocity of 2mm radius drop $=\frac{2g(\sigma -T)2^2}{9\eta }=4V$ [from(1)]
Now, Given, 4V= 20 cm/s
$\Rightarrow V=5cm/s$