Medium MCQ +4 / -1 PYQ · JEE Mains 2022

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

  1. A $\eta = {{4r\sigma g} \over {9v}}$
  2. B $\eta = {{2{r^2}\sigma g} \over {9v}}$ Correct answer
  3. C $\eta = {{2\pi {r^2}\sigma g} \over {9v}}$
  4. D $\eta = {{2{r^2}\sigma g} \over {3\pi v}}$

Solution

<p>Air bubble moves with constant speed v. So net force = 0.</p> <p>$\therefore$ Buoyant Force = Viscous force</p> <p>$\Rightarrow {F_b} = {F_v}$</p> <p>$\Rightarrow \sigma \times {4 \over 3}\pi {r^3}g = 6\pi nrv$</p> <p>$\Rightarrow n = {{2\sigma {r^2}g} \over {9v}}$</p>

About this question

Subject: Physics · Chapter: Properties of Solids and Liquids · Topic: Elasticity

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