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A boat of area 10 m2 floating on the surface of a river is made to move horizontally with a speed of 2 m/s by applying a tangential force. If the river is 1 m deep and the water in contact with the bed is stationary, find the tangential force needed to keep the boat moving with same velocity. (Assume the viscosity of water as 0.01 poise).

A
0.02 N
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B
0.03 N
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C
0.04 N
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D
0.05 N
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Solution

The correct option is A 0.02 N
Assuming linear velocity profile, velocity changes from 2 m/s at the surface to zero at the bed which is at a depth of 1 m
Velocity gradient =dvdy=201=2 s1
Now from Newton's law of viscous force,
|F|=ηAdvdy=(102×101)×10×2=0.02 N

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