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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(σ−ρ)ggη=2a2ρg9η⇒η=2a2ρg9v where, a = 5mm, ρ=1.4×103kg/m3,v=4mm/s ∴η=2×25×10−6×1.4×103×9.89×4×10−3kg/m−s=19.05kg/m−s Hence, (D) is correct.

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