A plate of area 2 m² is made to move horizontally with a speed of 2 m s⁻¹ by applying a horizontal tangential force over the free surface of a liquid. The depth of the liquid is 1 m and the liquid in contact with the bed is stationary. Coefficient of viscosity of liquid = 0.01 poise. The tangential force needed to move the plate is α × 10⁻³ N. Find the value of α.
Physics · Mixed Chapter
JEE Mains

Question

A plate of area 2 m² is made to move horizontally with a speed of 2 m s⁻¹ by applying a horizontal tangential force over the free surface of a liquid. The depth of the liquid is 1 m and the liquid in contact with the bed is stationary. Coefficient of viscosity of liquid = 0.01 poise. The tangential force needed to move the plate is α × 10⁻³ N. Find the value of α.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Newton’s law of viscosity gives F=η A(dv/dy) =η A(v/h). Step 2: Convert units: η=0.01 poise=0.001 Pa s. Step 3: F=0.001×2×(2/1)=0.004 N=4×10⁻³ N. Step 4: α=4.