Question

The terminal velocity of a rain drop of radius $r$ is $2cm{s}^{-1}$ . If eight such identical drops combine to form a single large drop, the terminal velocity would be

• A. $1cm{s}^{-1}$
• B. $2cm{s}^{-1}$
• C. $4cm{s}^{-1}$
• D. $8cm{s}^{-1}$

Answer 1

Answer: (D)

If eight drops of same radius $r$ coalesce, then radius of new drop is given by $R$.
$\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3$
$R=2r$
If drop of radius $r$ is falling in viscous medium, then it acquires a critical velocity $v$ and $v\propto r^2$
$\Rightarrow \frac{v_2}{v_1}={\left[\frac{R}{r}\right]}^2$
$={\left[\frac{2r}{r}\right]}^2=4$
$v_2=4v_1$
or $v_2=8cm{s}^{-1}$