`n` drops of water, each of radius `2 mm`, fall through air at a terminal velocity of `8 cm^(-1)` If they coalesce to form a single drop, then the terminal velocity of the combined drop is `32 cm^(-1)` The value of `n` is

Answer

8

Explanation

`4/3piR^(3)=nxx4/3pir^(3)`
or `R^(3)=nr^(3)` or `R=n^(1//3)r`
or `R=2pi^(1//3)mm`
`v_(0)propr^(2),v_(0)^(')propR^(2)`
Now `(v_(0)^('))/(v_(0))=(R^(2))/(r^(2))=(4n^(2//3))/4f`
or `32/8 =n^(2//3)` or `n^(2//3)=4`
or `n=4^(3//2)=sqrt(64)`
or `n=8`