Question

According to Newton viscus force is given by
$F=-\eta A \frac{d v}{d x}$
where $\eta=$ coefficient of viscosity, so dimensions of $\eta$ will be :

• A. $ [ML^{-1}T^{-2}]$
• B. $ [MLT^{-2}]$
• C. $ [ML^{-1}T^{-1}]$
• D. $ [M^{-1}L^{2}T^{-2}]$

Answer 1

Answer: (C)

$F=-\eta A \frac{d v}{d x}$
$\therefore \eta=-\frac{F}{A} \frac{d x}{d v}$
Writing the dimensions
$[\eta] =\frac{\left[ MLT ^{-2}\right]}{\left[ L ^{2}\right]} \frac{[ L ]}{\left[ LT ^{-1}\right]}$
$=\left[ ML ^{-1} T ^{-1}\right]$