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The velocity of water in river is 18kmph at the surface. If the river is 5m deep then the shearing stress between horizontal layers of water is____(Viscosity of water is $10^{- 3}$ poisuille).

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$10^{- 3} N / m^{2}$

$10^{- 4} N / m^{2}$

$10^{- 5} N / m^{2}$

$10^{- 2} N / m^{2}$

answer is B.

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Detailed Solution

Stress = $\frac{F}{A}$ $F = η A \frac{d v}{d x} \Rightarrow$ Stress $= η \frac{d v}{d x}$
Stress = $10^{- 3} \times \frac{5}{5} = 10^{- 3} N / m$ $(v = \frac{18 \times 5}{18} = 5 m / s)$

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