Question

A rectangular metal plate has dimensions of $10cm\times 20cm$. A thin film of oil separates the plate from a fixed horizontal surface. The separation between the rectangular plate and the horizontal surface is 0.2 mm. An ideal string is attached to the plate and passes over an ideal pulley to a mass m. When $m=125gm$, the metal plate moves at constant speed of 5 cm/s across the horizontal surface. Then the coefficient of viscosity of oil in $dyne-s/c{m}^2$ is $(Useg=1000cm/s^2)$:

• A. 5
• B. 2.5
• C. 25
• D. 50

Answer 1

Answer: (B)

2.5

Viscous force $F_{viscous}=\eta A\frac{dV}{dx}$

Velocity gradient $\frac{dV}{dx}=\frac{5}{0.02}=250$ ( mm to cm )

The weight of the block is equal to the viscous force when the block moves with a constant velocity.

$\therefore 125\times 1000=\eta \times (10\times 20)\times 250$

$\therefore \eta =2.5dyne-sc{m}^{-2}$