According to Newton, the viscous force acting between liquid layers of area A and velocity gradient Δ v/Δ Z is given by F = -η A(Δ v)/(Δ Z), where η is constant called coefficient of viscosity. The dimensional formula of η is (a) [ML⁻²T⁻²] (b) [M⁰L⁰T⁰] (c) [ML²T⁻²] (d) [ML⁻¹T⁻¹]

Answer: (d). η = (F)/(A (Δ v/Δ Z)). [Δ v/Δ Z] = T⁻¹, so [η] = MLT⁻²L²T⁻¹. [η] = ML⁻¹T⁻¹, so the answer is (d).

According to Newton, the viscous force acting between liquid layers… | NEET 1990 (AIPMT)

Q84NEET 1990 · AIPMTMedium

Applications of Dimensional Analysis

According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $\Delta v/\Delta Z$ is given by $F = -\eta A\frac{\Delta v}{\Delta Z}$ , where $\eta$ is constant called coefficient of viscosity. The dimensional formula of $\eta$ is

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Answer: (d)

$\eta = \dfrac{F}{A\,(\Delta v/\Delta Z)}$ .
$[\Delta v/\Delta Z] = T^{-1}$ , so $[\eta] = \dfrac{MLT^{-2}}{L^2T^{-1}}$ .
$[\eta] = ML^{-1}T^{-1}$ , so the answer is (d).

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