Question

According to Newton, the viscous force acting between liquid layers of area A and velocity gradient $\frac{\Delta \upsilon }{\Delta z}$ is given by $F=\eta A\frac{\Delta \upsilon }{\Delta z}$ where $\eta$ is a constant called coefficient of viscosity. The dimension of $\eta$ are:

• A. $\text{ }\\!\\![\\!\\!\text{ M}{{\text{L}}^{\text{2}}}{{\text{T}}^{\text{-2}}}\text{ }\\!\\!]\\!\\!\text{ }$
• B. $\text{ }\\!\\![\\!\\!\text{ M}{{\text{L}}^{\text{-1}}}{{\text{T}}^{\text{-1}}}\text{ }\\!\\!]\\!\\!\text{ }$
• C. $\text{ }\\!\\![\\!\\!\text{ M}{{\text{L}}^{-2}}{{\text{T}}^{-2}}\text{ }\\!\\!]\\!\\!\text{ }$
• D. $\text{ }\\!\\![\\!\\!\text{ }{{\text{M}}^{0}}{{\text{L}}^{0}}{{\text{T}}^{0}}\text{ }\\!\\!]\\!\\!\text{ }$

Answer 1

Answer: (B)

$\text{ }\\!\\![\\!\\!\text{ M}{{\text{L}}^{\text{-1}}}{{\text{T}}^{\text{-1}}}\text{ }\\!\\!]\\!\\!\text{ }$

Answer 2

Coefficient of viscosity $\eta =\frac{\text{force}\,\text{ }\\!\\!\times\\!\\!\text{ }\,\text{length}}{\text{area}\,\text{ }\\!\\!\times\\!\\!\text{ velocity}}$ Dimensions of $\eta$ $=\frac{\text{Dimension of}\,\text{force}\,\,\text{ }\\!\\!\times\\!\\!\text{ }\,\,\text{dimension of length}}{\text{Dimension of area}\,\,\text{ }\\!\\!\times\\!\\!\text{ }\,\,\text{dimension of velocity}}$ $=\frac{ML{{T}^{-2}}\times L}{{{L}^{2}}\times L{{T}^{-1}}}=[M{{L}^{-1}}{{T}^{-1}}]$