A metal plate of area $10^3 \mathrm{~cm}^2$ rests on a layer of 6mm thick. A tangential force of $10

Question

A metal plate of area $10^3 \mathrm{~cm}^2$ rests on a layer of 6mm thick. A tangential force of $10^{-2} \mathrm{~N}$ is applied on it to move it with a constant velocity $60 \mathrm{cms}^{-1}$. The coefficient of viscosity of the liquid is

Professor PC Thomas Classes · Answer

magnitude of viscous force $f=\eta A \frac{\mathrm{~d} v}{\mathrm{~d} x}$ velocity is constant so net force $=0$
$$
\begin{aligned}
& F-f=0 \
& \Rightarrow F=f \
& \Rightarrow F=\eta A \frac{\mathrm{~d} v}{\mathrm{~d} x} \
& \Rightarrow \eta=\frac{F}{A \frac{\mathrm{~d} V}{\mathrm{~d} x}} \
& 	herefore \eta=\frac{10^{-2}}{\left(10^3 	imes 10^{-4}ight)\left(\frac{6 	imes 10^{-2}}{6 	imes 10^{-3}}ight)} \
& =\frac{10^{-2} 	imes 6 	imes 10^{-3}}{10^{-1} 	imes 6 	imes 10^{-2}} \
& =10^{-2} \mathrm{Nsm}^2=0.1 	ext { poise }
\end{aligned}
$$