Question

A glass of slab of length 5 cm and breadth 2cm is kept on a thin layer of glycerin of thickness 1 mm. A horizontal force of 0.04 N is just sufficient to move the slab over glycerin with velocity 2 cm/s. Calculate neta

Answer 1

The length and breadth of the slab are $\sf{5\ cm}$ and $\sf{2\ cm}$ respectively.

Hence its area of contact with glycerin is,

$\sf{\longrightarrow A=5\ cm\times 2\ cm}$

$\sf{\longrightarrow A=10\ cm^2}$

$\sf{\longrightarrow A=10\times10^{-4}\ m^2}$

$\sf{\longrightarrow A=10^{-3}\ m^2}$

Thickness of glycerin is,

$\sf{\longrightarrow L=1\ mm}$

$\sf{\longrightarrow L=10^{-3}\ m}$

Velocity with which the slab moves over glycerin is,

$\sf{\longrightarrow v=2\ cm\,s^{-1}}$

$\sf{\longrightarrow v=2\times10^{-2}\ m\,s^{-1}}$

The force $\sf{0.04\ N}$ is sufficient to move the slab over glycerin. This means the viscous force is $\sf{F=0.04\ N=4\times10^{-2}\ N}$ and is given by,

$\sf{\longrightarrow F=\dfrac{A\,\eta\,v}{L}}$

Hence coefficient of viscosity is,

$\sf{\longrightarrow \eta=\dfrac{FL}{Av}}$

$\sf{\longrightarrow \eta=\dfrac{4\times10^{-2}\times 10^{-3}}{10^{-3}\times2\times10^{-2}}\ Pa\,s}$

$\sf{\longrightarrow\underline{\underline{\eta=2\ Pa\,s}}}$