JEE Main 2014 · 19 Apr · Shift 1 · Physics Q8

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The velocity of water in a river is 18 km/hr near the surface. If the river is 5 m deep, find the shearing stress between the horizontal layers of water. The co-efficient of viscosity of water $=10^{-2}$ poise.

10^{-1}

N/m

^2

10^{-2}

N/m

^2

10^{-3}

N/m

^2

10^{-4}

N/m

^2

Answer and worked solution

Official answer: C

Assuming the velocity falls linearly to zero at the bed: $\dfrac{dv}{dy}=\dfrac{5}{5}=1$ s⁻¹. With $\eta=10^{-2}$ poise $=10^{-3}$ Pa s:
$\tau=\eta\frac{dv}{dy}=10^{-3}\text{ N/m}^2.$

Topics:Viscosity and Stokes' law

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JEE Main 2014 · 19 Apr · Shift 1, Physics question 8