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Q.

Eight drops of water, each of radius 2 mm are falling through air at a terminal velocity of 8 cm s-1. If they coalesce to form a single drop, then the terminal velocity of combined drop will be

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a

30 cm s-1

b

24 cm s-1

c

32 cm s-1

d

28 cm s-1

answer is A.

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Detailed Solution

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Let the radius of bigger drop is R is smaller drop is r then

             43πR3 = 8×43×πR3

or R = 2r   ------(i)

Terminal velocity, v ∞ r2

v'v = R2r2 = (2rr)2  = 4

or v' = 4v = 4×8 = 32 cm s-1

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