If n identical water droplets falling under gravity with terminal velocity v coalesce to form single drop which has the terminal velocity 4v. Find the number n .

Explanation

To solve the problem, we need to find the number of identical water droplets, \( n \), that coalesce to form a single drop with a terminal velocity of \( 4v \) when the individual droplets have a terminal velocity of \( v \).

### Step-by-Step Solution:

1. **Understanding Terminal Velocity**:
The terminal velocity \( v \) of a droplet is given by the formula:
\[
v = \frac{2}{9} \frac{\rho - \sigma}{\eta} r^2 g
...