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JEE Main 20238 AprilMorning Shift
Exam
JEE Main
Year
2023
Date
8 April
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Main 2023 · 8 April · Morning Shift · Physics · Mechanical Properties of Fluids

An air bubble of diameter 6mm rises steadily through a solution of...

An air bubble of diameter 6mm6mm rises steadily through a solution of density 1750kgm−31750kg{m}^{- 3} at the rate of 0.35cms−10 . 35cm{s}^{- 1}. The co-efficient of viscosity of the solution (neglect density of air) is ________ Pas (given, g=10ms−2g = 10m{s}^{- 2}).

Correct answer

0

Step-by-step solution

The bubble is moving with a constant velocity so the net force acting on the body is zero.

Stokes' law defines the drag force which is given by F=6πηrvF = 6\piηrv

The buoyant force is given by B=Vρg=43πr3ρgB = Vρg = \dfrac{4}{3}\pi{r}^{3}ρg

Hence, it can be written that

43πr3ρg=6πηrv⇒η=2r2ρg9v=2×(3×10−3)2×1750×109×0.35×10−2=10Pas\dfrac{4}{3}\pi{r}^{3}ρg = 6\piηrv ⇒ η = \dfrac{2{r}^{2}ρg}{9v} = \dfrac{2 \times {\left(3 \times {10}^{- 3}\right)}^{2} \times 1750 \times 10}{9 \times 0 . 35 \times {10}^{- 2}} = 10Pas

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