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 0.75η0, at what minimum distance (in cm) from top wall 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).

Question

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 0.75η0​, at what minimum distance (in cm) from top wall 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).

Filo · Accepted Answer

Case I : y1​=y2​=h/2δyδu​=h/2v​=h2v​Viscous force=hη0​2V​AThe plate has two sides.Total force F=h4ηc​va​Case II: F=yηvA​+y−hηvA​=y(h−y)ηvAh​y(h−y)ηvAh​=h4v2Av​163​h2=y(h−y)Solving, we get y=4h​,43h​Hence, for minimum distance from top y=420​=5 cm.

Question Text	A thin plate $A B$ of large area $A$ is placed symmetrically in a small gap of height $h$ filled with water of viscosity $η_{0}$ 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 $0.75 η_{0}$ , at what minimum distance (in cm) from top wall 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 $h = 20 c m)$ .
Answer Type	Text solution:1
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