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Standard XII

Physics

Wave Equation

A gas bubble ...

Question

A gas bubble of $2 c m$ diameter rises through a liquid of density $1.75 g$ ${c m}^{- 3}$ with a fixed speed of $0.35 {c m s}^{- 1}$ . Neglect the density of the gas. The co-efficient of viscosity of the liquid is

870

poise

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1120

poise

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982

poise

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1089

poise

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Solution

The correct option is D $1089$ poise
Since the bubble rises with constant speed, the net force acting on the bubble must be zero.
Hence $V ρ g = 6 π η r v$ (Since the density of gas is negligible, its weight has no contribution)
$⟹ (\frac{4}{3} π 1^{3}) (1.75) (981) = 6 π η (1) (0.35)$
$⟹ η = 1089 p o i s e$

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A gas bubble of 2cm diameter rises through a liquid of density 1.75g cm−3 with a fixed speed of 0.35cms−1. Neglect the density of the gas. The co-efficient of viscosity of the liquid is

The correct option is D 1089 poiseSince the bubble rises with constant speed, the net force acting on the bubble must be zero.Hence Vρg=6πηrv(Since the density of gas is negligible, its weight has no contribution)⟹(43π13)(1.75)(981)=6πη(1)(0.35)⟹η=1089poise

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