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)
see full answer
Your Exam Success, Personally Taken Care Of
1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.
An Intiative by Sri Chaitanya
answer is 5.
(Unlock A.I Detailed Solution for FREE)
Best Courses for You
JEE
NEET
Foundation JEE
Foundation NEET
CBSE
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