An air bubble of negligible weight having radius r rises steadily through a of density σ at speed v. The coefficient of viscosity of the is given by: (a) η = (4rσ g)/(9v) (b) η = (2r²σ g)/(9v) (c) η = (2π r²σ g)/(9v) (d) η = (2r²σ g)/(3π v)

Answer: (b). Bubble weight negligible: upthrust 4/3π r³σ g balances viscous drag 6πη r v. η = (4π r³σ g)/(3 × 6π r v) = (2r²σ g)/(9v) So the answer is (b).

An air bubble of negligible weight having radius r rises steadily… | JEE Main 2022 (30 Jun, Shift 1)

Q40JEE Main 2022 · 30 JUN · SHIFT 1Medium

Terminal Velocity

An air bubble of negligible weight having radius r rises steadily through a of density $\sigma$ at speed v. The coefficient of viscosity of the is given by:

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Answer: (b)

Bubble weight negligible: upthrust $\frac{4}{3}\pi r^3\sigma g$ balances viscous drag $6\pi\eta r v$ .
$\eta = \dfrac{4\pi r^3\sigma g}{3 \times 6\pi r v} = \dfrac{2r^2\sigma g}{9v}$
So the answer is (b).

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Terminal Velocity question from JEE Main 2022 (30 Jun, Shift 1)

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