A plate of area 2 m2 is made to move horizontally with a speed of 2 ms-1 by applying a horizontal tangential force over the free surface of a liquid. The depth of the liquid is 1 m and the liquid in contact with the bed is stationary. Coefficient of viscosity of liquid = 0.01 poise. The tangential force needed to move the plate is α x 10-3 N. The valve of α is________.
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answer is 4.
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Detailed Solution
Velocity gradient =ΔvΔy=2−01−0=2ms−1m−1 Viscous force, |F|=ηAΔvΔy=0.01×10−1(2)(2)=0.004NSo, to keep the plate moving with constant velocity, a force of 4 x 10-3N has to be applied. Thus, α = 4.