Q. Which one of the following represents the correct dimensions of the coefficient of viscosity?
A) $\left\lbrack {ML}^{- 1}T^{- 2} \right\rbrack$
B) $\left\lbrack {MLT}^{- 1} \right\rbrack$
C) $\left\lbrack {ML}^{- 1}T^{- 1} \right\rbrack$
D) $\left\lbrack {ML}^{- 2}T^{- 2} \right\rbrack$
Explanation
By Newton’s formula $\eta = \frac{F}{A\left( \mathrm{\Delta}v_{x}/\mathrm{\Delta}z \right)}$ $\therefore Dimensions\ of\ \ \eta$ $\ \ \ \ = \frac{dimensions\ of\ force}{\begin{array}{r} dimensions\ of\ area\ \times dimensions\ of\ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ velocity\ gradient \end{array}}$ $\ \ \ \ = \frac{\left\lbrack MLT^{- 2} \right\rbrack}{\left\lbrack L^{2} \right\rbrack\left\lbrack T^{- 1} \right\rbrack} = \left\lbrack ML^{- 1}T^{- 1} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.