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Question

Two drops of same radius are falling through air with a steady velocity of 5 cm/s. If the two drops coalesce, the terminal velocity will be

A
10 cm/s
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B
2.5 cm/s
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C
5×(4)1/3 cm/s
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D
5×2 cm/s
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Solution

The correct option is C 5×(4)1/3 cm/s
Terminal velocity for a spherical body of radius R and density ρ falling in a liquid of density σ and dynamic viscosity η is given by,
VT=29(ρσ)R2gη
VTR2
Let two identical drops of radius R1 coalesce to form bigger drop of radius R2,
VT2VT1=R22R21(1)
Since the volume remains same before and after the drops coalesce. Therefore,
Vi=Vf
2×43πR31=43πR32
R2=(2)1/3R1
Substituting this in equation (1),
VT2VT1=(4)1/3R21R21
VT2=5×(4)1/3 cm/s

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