Question

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

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

Answer 1

Answer: (C)

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