Question

Two drops of same radius are falling through air with steady velocity $v$. If the two drops coalesce, what would be the terminal velocity?

• A. $4v$
• B. $(4{)}^{1/3}v$
• C. $2v$
• D. $64v$

Answer 1

The correct option is B $(4{)}^{1/3}v$

Let $r$ be the radius of each drop and $R$ be radius of coalesed drop
$\because$ terminal velocity
$v=\frac{2}{9\eta }{r}^2(\rho -\sigma )g$
$v\propto r^2$
$v=k{r}^2$
Initial volume = final volume
$2\frac{4}{3}\pi r^3=\frac{4}{3}\pi R^3$
$R=2^{1/3}.r$
$V^{\prime }\propto R^2$
$V^{\prime }\propto (2^{1/3}r{)}^2$
$V^{\prime }\propto 4^{1/3}{r}^2$
$V^{\prime }\propto 4^{1/3}v$.