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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 m...

There is a 1 mm thick layer of oil between a flat plate of area 10−2m210^{-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

0.015 N

Explanation

Solution

Step-by-Step Solution

We use the formula for viscous force:

F=ηAvdF = \eta A \frac{v}{d}

Given:

  • η=1 poise=0.1 Pa⋅s\eta = 1 \text{ poise} = 0.1\, \text{Pa}\cdot\text{s}
  • A=10−2 m2A = 10^{-2}\, \text{m}^2
  • v=1.5 cm/s=1.5×10−2 m/sv = 1.5\, \text{cm/s} = 1.5\times10^{-2}\, \text{m/s}
  • d=1 mm=1×10−3 md = 1\, \text{mm} = 1\times10^{-3}\, \text{m}

Calculation:

vd=1.5×10−21×10−3=15 s−1\frac{v}{d} = \frac{1.5\times10^{-2}}{1\times10^{-3}} = 15\, \text{s}^{-1} F=(0.1)×(10−2)×(15)=0.1×0.01×15=0.015 NF = (0.1)\times(10^{-2})\times(15) = 0.1\times0.01\times15 = 0.015\, \text{N}

Since the computed force is 0.015 N0.015\, \text{N}, which does not match any provided numerical option, the correct answer is: 0.015 N