Question

A space $2.5 cm$ 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 $kg - s / m ^{2}$ is:

• A. $5 \times 10^{-2}$
• B. $2.5 \times 10^{-2}$
• C. $1 \times 10^{-2}$
• D. $7.5 \times 10^{-2}$

Answer 1

Answer: (B)

Velocity gradient $=\frac{0.5}{\frac{2.5}{2} \times 10^{-2}}$
As force on the plate due to viscosity is from upper as well as lower portion of the oil, equal from each part,
Then, $F=2 \eta A \frac{d v}{d z}$
$=2 \times \eta \times(0.5) \frac{0.5}{1.25 \times 10^{-2}}$

$\Rightarrow \eta=2.5 \times 10^{-2} kg - sec / m ^{2}$