Question

The correct dimensions of the coefficient of viscosity $\eta$ are

• A. $\left[ ML ^{-1} T ^{-2}\right]$
• B. $\left[ MLT ^{-1}\right]$
• C. $\left[ ML ^{-1} T ^{-1}\right]$
• D. $\left[ ML ^{-2} T ^{-2}\right]$

Answer 1

Answer: (C)

Viscous force is given as, $F =6 \pi \eta rv$.
$\therefore \eta=\frac{ F }{6 \pi rv }$
$[\eta]=\frac{[ F ]}{[ r ][ v ]}$
$[\eta]=\frac{\left[ MLT ^{-2}\right]}{[ L ]\left[ LT ^{-1}\right]}$