A plate sliding at speed v on a liquid layer of thickness d requires horizontal force F. Now the same plate lies midway between two fixed surfaces in a liquid layer of thickness d, moving at same speed. Required force is kF. Find k.
Physics · Mixed Chapter
JEE Main Practice

Question

A plate sliding at speed v on a liquid layer of thickness d requires horizontal force F. Now the same plate lies midway between two fixed surfaces in a liquid layer of thickness d, moving at same speed. Required force is kF. Find k.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Newton’s viscosity law for one wetted surface is F = η A(v/d). Step 2 — When plate lies halfway between two fixed surfaces, its two liquid gaps each have thickness d/2. Step 3 — Each face then experiences ηAv/(d/2) = 2F. Step 4 — Total force from both faces is 2F + 2F = 4F; therefore k = 4.