Question: Dimensions of coefficient of viscosity are: [PMT/NEET-1993]
a. $ML^{2}T^{-2}$
b. $ML^{2}T^{-1}$
c. $ML^{-1}T^{-1}$
d. $MLT$

Solution
Coefficient of viscosity $\eta$ appears in Newton’s law of viscosity:
$
F = \eta A \frac{dv}{dx}
$
$
\eta = \frac{F}{A \cdot (dv/dx)}
$

Dimensions:

• $F = MLT^{-2}$
• $A = L^{2}$
• $\dfrac{dv}{dx} = \dfrac{LT^{-1}}{L} = T^{-1}$

$
[\eta] = \frac{MLT^{-2}}{L^{2} \cdot T^{-1}} = \frac{MLT^{-2}}{L^{2}T^{-1}} = ML^{-1}T^{-1}
$

Answer
c. $ML^{-1}T^{-1}$