27 identical drops of water are falling down vertically in air with terminal velocity `0.10ms^(-1)` What will be its terminal velocity if they combine to form a bigger drop?

Explanation

We are given: `v=0.10ms^(-1)`
We know that, terminal velocity of the drop having radius r is given by
`v=(2)/(9)(r^(2)(rho-sigma))/(eta)g" ".......(i)`
Also, volume of bigger drop = volume of 27 small drops
`(4)/(3)piR^(3)=27xx(4)/(3)pir^(3)`or R=3r
We are to find, Terminal velocity of the drop having radius R.
Terminal velocity of bigger drop,
`v.=(2)/(9)(R^(2)(rho-sigma))/(eta)g" ".......(ii)`
Dividing equation (ii) by (i)
`(v.)/(v)=((R)/(r))^(2)=9` or `v.=9xx0.10=0.9ms^(-1)`