Question

A big drop of radius $R$ is formed by 729 small drops of water of radius $r$, then the radius of each small drop will be :

• A. $\frac{R}{9}$
• B. $\frac{R}{900}$
• C. $\frac{R}{1800}$
• D. $\frac{R}{9000}$

Answer 1

The correct option is A $\frac{R}{9}$

Equating volume in both cases,
$\frac{4}{3}\pi R^3=729\times \frac{4}{3}\pi r^3$
$\Rightarrow r^3=\frac{R^3}{729}$
$\Rightarrow r=\frac{R}{9}$