Question

Two drops of the same radius are falling through air with a steady velocity of 5 cm per sec. If the two drops coalesce, the terminal velocity would be

• A. 10 cm per sec
• B. 2.5 cm per sec
• C.
• D.

Answer 1

The correct option is C

If two drops of same radius r coalesce then radius of new drop is given by R
$\frac{4}{3}\pi R^3=\frac{4}{3}\pi r^3+\frac{4}{3}\pi r^3\Rightarrow R^3=2r^3\Rightarrow R=2^{1/3}r$
If drop of radius r is falling in viscous medium then it acquire a critical velocity v and $v\propto r^2$ $\frac{v_2}{v_1}={\left(\frac{R}{r}\right)}^2={\left(\frac{2^{1/3}r}{r}\right)}^2\Rightarrow v_2=2^{2/3}\times v_1=2^{2/3}\times \left(5\right)=5\times {\left(4\right)}^{1/3}cm/s$