Question

8 rain drops of radius 1 mm each falling down with terminal velocity of 5 cm/s coalesce to form a bigger drop.Find the terminal velocity of bigger drop

Answer 1

Given, radius of each small drop = 1 mm = 0.1 cm

Let the radius of bigger drop be R and small drops be r.

The 8 drops form a bigger drop,but their volumes will remain equal i.e,

Volume of bigger drop = Volume of 8 small drops

4/3πR³ = 8 x 4/3πr³
R³ = 8r³
R = 2r = 2 x 0.1 = 0.2 cm

Terminal velocity of each small drop, v = 2/9 r²/η [ρ - ρ']g

Terminal velocity of bigger drop, V = 2/9 R²/η [ρ -ρ']g

Now dividing V by v we get,

V/v = R²/r²
V = v x R²/r²
V = 5 x 0.04/0.01
V = 5 x 4 = 20 cm/s

Hence required velocity is 20 cm/s

Hope This Helps You

Answer 2

Please see my answer also

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by looking at this photo it seems to be very dirty but you will understand the answer very clearly

:)

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