Eight equal drops of water are falling through air with a steady velocity of 10 cm`s^(-1)`.If the drops combine to form a single drop big in size,then the terminal velocity of this big drop is

Options

A. 40 cm `s^(-1)`
B. 10 cm `S^(-1)`
C. 30 cm `s^(-1)`
D. 80 cm `s^(-1)`

Answer

A

Explanation

Let r be radius of each small water droplet and R be radius of a big drop formed volume of big drop =`8xx "volume"` of each small droplet
`(4)/(3)piR^(3)8xx(4)/(3)pir^(3)`
R=2r
Let terminal velocity of small droplet be`v_(1)` and of big drop be `v_(2)`
Terminal velocity ,v`(2)/(9)(r^(2)(rho-sigma)g)/(eta)`
Where the symbols have their usual meaning `therefore c prop r^(2)`
`therefore (v_(2))/(v_(1))=(R^(2))/(r^(2))`
or `v_(2)=v_(1)((R)/(r))^(2)=v_(1)((2r)/(r))^(2)=4v_(1)=4xx10cm s^(-1)`
=40 cm`S^(-1)`