| A thin movable plate is separated from two fixed plates \[{{P}_{1}}\]and \[{{P}_{2}}\] by two highly viscous liquids of coefficients of viscosity \[{{n}_{1}}\] and \[{{n}_{2\,}}\] as shown where \[{{n}_{2}}=9{{n}_{1}}.\]Area of contact of movable plate with each fluid is same. If the distance between two fixed plates is h, then the distance \[{{h}_{1}}\] movable plate form upper plate such that movable plate can be moved with a finite velocity by applying the minimum possible force on movable plate is (assume only linear velocity distribution in each liquid) |
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A) \[\frac{h}{4}\]
B) \[\frac{h}{2}\]
C) \[\frac{h}{6}\]
D) \[\frac{h}{3}\]
Correct Answer: A
Solution :
\[F=\left[ {{n}_{1}}\frac{v}{{{h}_{1}}}+{{n}_{2}}\frac{v}{\left( h-{{h}_{1}} \right)} \right]{{ & }_{A}}\] \[\frac{dF}{d{{h}_{1}}}=0\] \[{{h}_{1}}=\frac{h}{4}\]
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