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/sTerminal velocity , vT=2r2(σ−ρ)g9η where σ→ density of body falling through the given fluid of density ρ ⇒vT∝r2 Let the terminal velocity for smaller drop (r) and bigger drop (R) be vT and v′T respectively. ∴vTv′T=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), 10v′T=r2(2r)2=14 Terminal velocity of bigger drop will be v′T=4×vT=40 cm/s

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