Fluid Mechanics

JEE Main level, numerical answer, medium

130 of 192

Question 130 of 192

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes 0.01cm30.01{cm}^{3} of oleic acid per cm3{cm}^{3} of the solution. Then you make a thin film of this solution (monomolecular thickness) of area 4cm24{cm}^{2} by considering 100100 spherical drops of radius (340π)13×10−3cm.{\left(\dfrac{3}{40\pi }\right)}^{\dfrac{1}{3}}\times {10}^{-3}cm. Then the thickness of oleic acid layer will be x×10−14mx\times {10}^{-14}m. Where xx is ________ .

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Answer: 25

4tT=100×43πr34{t}_{T}=100\times \dfrac{4}{3}\pi {r}^{3}
=100×4π3×340π×10−9=10−8cm3=100\times \dfrac{4\pi }{3}\times \dfrac{3}{40\pi }\times {10}^{-9}={10}^{-8}{cm}^{3}
tT=25×10−10cm{t}_{T}=25\times {10}^{-10}cm=25×10−12m=25\times {10}^{-12}m
t0=0.01tT=25×10−14m{t}_{0}=0.01{t}_{T}=25\times {10}^{-14}m⇒x=25\Rightarrow x=25.

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