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A space 2.5 cm wide between two large plane surfaces is filled

Question

A space $2.5 c m$ wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area $0.5 m^{2}$ just midway the surfaces at a speed of $0.5 m / sec$ is $1 N$ . The coefficient of viscosity in $k g s / m^{2}$ is:

5 \times 1 0^{- 2}

2.5 \times 1 0^{- 2}

1 \times 1 0^{- 2}

7.5 \times 1 0^{- 2}

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Henry Discussed

A space

2.5 c m

wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area

0.5 m^{2}

just midway the surfaces at a speed of

0.5 m / sec

1 N

. The coefficient of viscosity in

k g s / m^{2}

is:

15 mins ago

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15 mins ago

Text solutionVerified

Velocity gradient

\frac{d V}{d z} = \frac{0.5}{\frac{2.5}{2} \times 1 0 ^{- 2}} = 40

As force on the plate due to viscosity is from upper as well as lower portion of the oil, and both are equal, using the expression for viscous force,

F_{v i sco u s} = η A \frac{d V}{d z}

Since there are two surfaces, we get

F_{v i sco u s} = η \times 2 A \frac{d V}{d z}

∴ 1 N = ∴ η \times 2 \times 0.5 \times 40

∴ η = 2.5 \times 1 0^{- 2} k g sec m^{- 2}

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Question Text	A space $2.5 c m$ wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area $0.5 m^{2}$ just midway the surfaces at a speed of $0.5 m / sec$ is $1 N$ . The coefficient of viscosity in $k g s / m^{2}$ is:
Answer Type	Text solution:1
Upvotes	150