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An air bubble of radius 5mm rises throug...

An air bubble of radius `5mm` rises through a vat of syrup at a steady speed `2mm//s`. If the syrup has a density of `1.4xx10^(3)kg//m^(3)`, what is its velocity ?

A

`1.15 kg//m-s`

B

`15 kg//m-s`

C

`2.25 kg//m-s`

D

`19.05 kg//m-s`

Text Solution

Verified by Experts

In this case the terminal velocity is upward. Since `sigma gt rho`, the density of the air inside the bubble may be neglected completely.
From equation
`v=(2a^(2)(rho-sigma)g)/(9eta)=(2a^(2)rhog)/(9eta)`
`rArr eta=(2a^(2)rhog)/(9v)`, where `a=00.005mm`, `rho=1.4xx10^(3)kg//m^(3)`, `v=0.004m//s`
`: eta=(2xx25xx10^(-6)xx1.4xx10^(3)xx9.8)/(9xx4xx10^(-3))kg//m-s=19.05kg//m-s`
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