First slide

Dimensions of physical quantities

Question

Find the dimensional formula of coefficient of viscosity $η$ .

Moderate

A

$[{ML}^{- 1}]$
B

$[ML T^{- 1}]$
C

$[{ML}^{- 1} T^{- 1}]$
D

$[{ML}^{- 1} T^{- 2}]$

Solution

A denotes the area, v the velocity, l is the length.
$η = - \frac{F}{A} \frac{Δ l}{Δ v} \Rightarrow ∴ [η] = \frac{[F] [l]}{[A] [v]} = \frac{[{MLT}^{- 2}] [L]}{[L^{2}] [{LT}^{- 1}]} = [{ML}^{- 1} T^{- 1}]$

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