Physics - Unit & Dimension Question with Solution | TestHub

Coefficient of viscosity$\left(\mathrm{\eta }\right)=\frac{\mathrm{F}\mathrm{x}}{\mathrm{A}\mathrm{v}}$

F = tangential Force,

A = Area, x = distance between the layers,

v = velocity.

Dimensional Formula of Force$={\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-2}$

Dimensional Formula of Area$={\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^0$

Dimensional Formula of distance${=\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0$

Dimensional Formula of velocity$={\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^{-1}$

Putting these values in above equation we get,

$\left[\mathrm{\eta }\right]=\frac{\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-2}\right]\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^0\right]}{\left[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^0\right]\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^{-1}\right]}=\left[{\mathrm{M}}^1{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}\right]$