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JEE Main 2022 · 25 Jun · Shift 1, Physics question 53

The velocity of upper layer of water in a river is 36 kmh−136\ \mathrm{kmh^{-1}}. Shearing stress between horizontal layers of water is 10−3 Nm−210^{-3}\ \mathrm{Nm^{-2}}. Depth of the river is ______ m. (Co-efficient of viscosity of water is 10−210^{-2} Pa.s)

Answer and worked solution

Official answer: 100

Viscous stress. τ=ηvd\tau=\eta\dfrac vd with v=36v=36 km h−1=10^{-1}=10 m s−1^{-1}.

Depth. d=ηvτ=10−2×1010−3=100d=\dfrac{\eta v}\tau=\dfrac{10^{-2}\times10}{10^{-3}}=100 m.

Answer: 100

Topics:Viscosity and Stokes' law
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