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Question

Eight small drops of equal size are falling through air with a steady velocity of 10 cm/sec. If the drops coalesce, what would be the terminal velocity of the bigger drop?

A
40 cm/s
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B
20 cm/s
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C
30 cm/s
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D
50 cm/s
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Solution

The correct option is A 40 cm/s
Terminal velocity , vT=2r2(σρ)g9η
where σ density of body falling through the given fluid of density ρ
vTr2
Let the terminal velocity for smaller drop (r) and bigger drop (R) be vT and vT respectively.
vTvT=r2R2 ...(i)

After the small drops coalesce, Volume of the big drop=8×Volume of each small drop
43πR3=8×43πr3
R=2r
Given, terminal velocity (steady velocity) of small drop is vT=10 cm/s
Substituting in Eq.(i),
10vT=r2(2r)2=14
Terminal velocity of bigger drop will be
vT=4×vT=40 cm/s

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