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According to Newton, the viscous force acting between liquid layers of area A and velocity gradient ΔV/ΔZ is given by \( F = -ηA \frac{ΔV}{ΔZ} \) where η is constant called coefficient of viscosity. The dimensional formula of η is

1. ML⁻²T⁻²
2. M⁰L⁰T⁰
3. ML⁻²T⁻²
4. ML⁻¹T⁻¹

Correct answer: ML⁻¹T⁻¹

Solution

From F = ηA(ΔV/ΔZ), the dimensions of η are [F]/([A][ΔV/ΔZ]). Since force is MLT⁻², area is L², and velocity gradient is T⁻¹, η becomes ML⁻¹T⁻¹. This is the standard dimension of coefficient of viscosity.

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