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Two spherical raindrops of equal size ar...

Two spherical raindrops of equal size are falling vertically through air with a velocity of `1 m//s`. What would be the terminal speed if these two drops were to coalesce to form a large spherical drop?

Text Solution

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`V_(T) prop r^(2)`
Let r be the radius of small rain drops and R the radius of the large drop.
Equating the volumes, we have
`( 4)/( 3) pi R^(2) = 2 ((4)/( 3) pi r^(3))`
`:. R= ( 2) ^(1//3) r` or ` (R )/( r) = ( 2)^(1//3)`
`:. ( V_(T)')/(V_(T))= (( R )/( r ))^(2) = ( 2)^(2//3)`
`:. V_(T ) ' = ( 2)^(2//3) V_(T) = ( 2) ^(2//3) ( 1.0) m//s`
`= 1.587 m//s`
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