Question

two equal drops of water each of radius $r$ are falling through air with a steady velocity $8cm/s$. the two drops combine to form a big drop. The terminal velocity of big drop will be:

• A. $8(2{)}^{\frac{2}{3}}cm/s$
• B. $16(2{)}^{\frac{2}{3}}cm$
• C. $4(2{)}^{\frac{2}{3}}cm$
• D. $32cm/s$

Answer 1

The correct option is A $8(2{)}^{\frac{2}{3}}cm/s$

$V=\frac{mg}{6\pi hr\theta }$
$S=\frac{mg}{6\pi hrv}$
$2\left[\frac{4}{3}\pi r^3\right]g=\frac{4}{3}\pi R^{3}g$
$R=2^{\frac{9}{3}}r$
$V_1=\frac{2mg}{6\pi hR}$
$V_1=\frac{2mg}{6\pi hr}$
$=2\times 8$
$V_1=8\times (2{)}^{2/3}cm/sec$