Q 11-09-103JEE MainJEE Main 2022 (25 Jun, Shift 1)Easy
The velocity of the upper layer of water in a river is $36\ \text{km h}^{-1}$. Shearing stress between horizontal layers of water is $10^{-3}\ \text{N m}^{-2}$. Depth of the river is ______ m. (Coefficient of viscosity of water is $10^{-2}\ \text{Pa s}$)
Numerical value type. Enter your answer.
Answer: 100
With the bottom layer at rest, the velocity gradient is $\dfrac vd$, and stress $= \eta\dfrac vd$:
$$d = \frac{\eta v}{\text{stress}} = \frac{10^{-2}\times10}{10^{-3}} = 100\ \text{m}$$
Solution by Sreeraj P, M.Sc Physics