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Q.

A thin plate AB of large area A is placed symmetrically in a small gap of height 'h' filled with water of viscosity η0 and the plate has a constant velocity v by applying a force F, as shown in the figure. If the gap is filled with some other liquid of viscosity 0.75 η0 where should the plate be placed in the gap, so that the plate can again be pulled at the same constant velocity V, by applying the same force F. (Take h = 20 cm)

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answer is 5.

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Detailed Solution

Case I: y1=y2=h/2∂u∂y=vh/2=2vh Viscous force =η02VhAThe plate has got two sides.  Total force F=4ηcvah  Case II: F=ηvAy+ηvAy−h=ηvAhy(h−y) ηvAhy(h−y)=4n2Avh;316h2=y(h−y) Solving we get y=h4,3h4Hence, for minimum distance from top y=20/4= 5 cm
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