Question

Two round rain 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
$\frac{4}{3}\pi R^3=\frac{4}{3}\pi r^3+\frac{4}{3}\pi r^3\Rightarrow R^3=2r^3\Rightarrow =2^{\frac{1}{3}}r$
If drop of radius r is falling in viscous media the it acquires a critical velocity v and $v\propto r^2$
$\frac{v_2}{v_1}=(\frac{R}{r}{)}^2=(\frac{2^{1/3}r}{r}{)}^2$
$\Rightarrow v_2=2^{\frac{2}{3}}\times v_1=2^{\frac{2}{3}}\times \left(5\right)=5\times (4{)}^{\frac{1}{3}}cm/s$