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A large wooden plate of area 10 m² floats on a river and is dragged horizontally at 2 m/s by a tangential force. The river is 1 m deep and water in contact with the bed is at rest. The coefficient of viscosity of water is 10⁻² poise. Find the tangential force needed to keep the plate moving.
- 15 mN
- 18 mN
- 20 mN
- 23 mN
Correct answer: 20 mN
Solution
The viscous drag equals eta times area times velocity gradient. The velocity drops linearly from 2 m/s at the plate to 0 at the bed over 1 m depth.
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