A thin plate `AB` of large area `A` is placed symmetrically in a small gap of height `h` filled with water of viscosity `eta_(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 eta_(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 cm`)

Answer

5

Explanation

Case I : `y_(1)=y_(2)=h/2`
`(delu)/(dely)=v/(h//2)=(2v)/h`

Viscous force `=(eta_(0)2V)/hA`
The plate has two sides.
Total force `F=(4eta_(c)va)/h`
Case II:
`F=(etavA)/y+(etavA)/(y-h)=(etavAh)/(y(h-y))`
`(etavAh)/(y(h-y))=(4v^(2)Av)/h`
`=3/16h^(2)=y(h-y)`
Solving we get
`h=h/3, (3h)/4`
Hence for minimum distance from top `=0/4=5cm`