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Question

An air bubble of radius 5mm rises through a vat of syrup at a steady speed of 4mm/s. If the syrup has a density of 1.4×103kg/m3, what is its viscosity?


A

1.15 kg/m-s

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B

15kg/m-s

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C

2.25 kg/m-s

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D

19.05 kg/m-s

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Solution

The correct option is D

19.05 kg/m-s


In this case the terminal velocity is upward. Since σ>ρ, the density of the air

inside the bubble may be neglected completely.

From equation

v=2a2(σρ)ggη=2a2ρg9ηη=2a2ρg9v

where, a = 5mm, ρ=1.4×103kg/m3,v=4mm/s

η=2×25×106×1.4×103×9.89×4×103kg/ms=19.05kg/ms

Hence, (D) is correct.


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