Question

Eight identical drops of water falling through air with uniform velocity of $10cm/s$ combine to form a single drop of big size, then terminal velocity of the big drop will be

• A. $80cm/s$
• B. $10cm/s$
• C. $30cm/s$
• D. $40cm/s$

Answer 1

Answer: (D)

Given, terminal velocity of each small drop
$v_1=10cm/s$
When 8 small drops are combined to form bigger drop, then volume will be same. If $r_1$ be radius of small drop and $r_2$ be radius of bigger drop, then $v_2=v_1$
$\frac{4}{3}\pi r_2^3=8\times \frac{4}{3}\pi r_1^3\Rightarrow r_2=2r_1$
$\therefore$ Terminal velocity of the drop
$v=\frac{2}{9}\frac{r^2(\rho -\sigma )}{9\eta }$
i.e., $v\propto r^2$
$\therefore \frac{v_1}{v_2}=\frac{r_1^2}{r_2^2}=\frac{r_1^2}{{\left(2r_1\right)}^2}\Rightarrow \frac{v_1}{v_2}=\frac{1}{4}$
$v_2=4v_1=4\times 10=40cm/s$