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A large wooden plate 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. River is 1 m deep and the water in contact with the bed is stationary. Then choose correct statement. (coefficient of viscosity of water = 10^-3 N-s/m²)

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Velocity gradient is 2 s^-1

Velocity· gradient is 1 s^-1

Force required to keep the plate moving with constant speed is 0.02 N

Force required to keep the plate moving with constant speed is 0.01 N

answer is A, C.

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Detailed Solution

$V e l o c i t y g r a d i e n t = \frac{∆ v}{∆ h} = \frac{2 m / s}{1 m} = 2 s^{- 1} F = η A \frac{∆ v}{∆ h} = (10^{- 3}) (10) (2) = 0.02 N$

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