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

Verified by Experts

As, `v_(T) prop r^(2)`
Let r be the radius of small raindrops and R the radius of large drop.
Equating the volumes, we have
`(4)/(3) piR^(3)=2((4)/(3) pi r^(3))`
`therefore " " R=(2)^(1//3). R " or " (R )/(r )=(2)^(1//3)`
`therefore " " (v'_(T))/(v_(T))=(( R)/(r ))^(2)=(2)^(2//3)`
`therefore " " v'_(T)=(2)^(2//3)v_(T)=(2)^(2//3) (1.0) ms^(-1)=1.587 ms^(-1)`

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