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Question

# An air bubble of diameter 4 mm rises steadily through a solution of density 1800 kg/m3 at the rate of 0.05 m/s. Neglecting density of air, the co-efficient of viscosity of the solution is [Take g=10 m/s2]

A
0.64 poise
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B
6.4 poise
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C
0.32 poise
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D
3.2 poise
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Solution

## The correct option is D 3.2 poiseGiven, diameter of air bubble, d=4 mm Radius of air bubble, r=2 mm=2×10−3 m Density of solution, ρ=1800 kg/m3 Speed of air bubble, v=0.05 m/s Co-efficient of viscosity of solution, η=? As air bubble rises steadily, therefore net force on it should be zero. Also, density of the air is neglegile, so we can neglect force due to gravity. ∑F=0 ⇒Fb−Fv=0 ⇒43πr3ρg=6πηrv ⇒η=2r2ρg9v =2×(2×10−3)2×1800×109×0.05 ⇒η=0.32 Pa-s=3.2 poise

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