Q. According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $\mathrm{\Delta}v/\mathrm{\Delta}z$ is given by $F = - \eta A\frac{\Delta v}{\Delta x}$ where $\eta$ is constant called coefficient of viscosity. The dimensions of $\eta$ are
A) $\lbrack ML^{2}T^{- 2}\rbrack$
B) $\lbrack ML^{- 1}T^{- 1}\rbrack$
C) $\lbrack ML^{- 2}T^{- 2}\rbrack$
D) $\lbrack M^{0}L^{0}T^{0}\rbrack$
Explanation
$F = - \eta A\frac{\Delta v}{\Delta z} \Rightarrow \lbrack\eta\rbrack = \lbrack ML^{- 1}T^{- 1}\rbrack$ As $F = \left\lbrack MLT^{- 2} \right\rbrack,\ A = \left\lbrack L^{2} \right\rbrack,\frac{\Delta v}{\Delta z} = \lbrack T^{- 1}\rbrack$ $\therefore$ Dimensions of $\eta = \frac{F}{A}\frac{\Delta z}{\Delta v} = \frac{MLT^{- 2}}{L^{2}}.\frac{1}{T^{- 1}} = \lbrack ML^{- 1}T^{- 1}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.