Question

There is a 1 mm thick layer of oil between a flat plate of area 10$^{-2}$ m$^2$ and a big plate. How much force is required to move the plate with a velocity of 1.5 cm/s²? The coefficient of viscosity of oil is 1 poise

• A. None of these

Answer 1

Answer: (A)

None of these

Answer 2

Using Newton’s law of viscosity, the viscous force is given by

$$F = \eta A \frac{v}{d}$$

where
$\eta = 1\, \text{poise} = 0.1\, \text{kg/(m·s)}$
$A = 10^{-2}\, \text{m}^2$
$v = 1.5\, \text{cm/s} = 0.015\, \text{m/s}$
$d = 1\, \text{mm} = 0.001\, \text{m}$

Substitute the values:

$$F = 0.1 \times 10^{-2} \times \frac{0.015}{0.001} = 0.1 \times 10^{-2} \times 15 = 0.1 \times 0.15 = 0.015\, \text{N}$$

Since none of the provided options match 0.015 N, the correct answer is:

Answer: (4) None of these

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Explanation (Minimal):
Use $F = \eta A \frac{v}{d}$ with $\eta = 0.1$ kg/(m·s), $A = 10^{-2}$ m², $v = 0.015$ m/s, $d = 0.001$ m. Calculation gives $F=0.015\,{\rm N}$.