Which pair correctly gives the dimensions and SI unit of the coefficient of dynamic viscosity η?
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Question

Which pair correctly gives the dimensions and SI unit of the coefficient of dynamic viscosity η?

G1 Physics · Accepted Answer

Using Newton's law of viscosity, F = ηA(dv/dy). Therefore, η = F/[A(dv/dy)]. Now, [F] = MLT⁻², [A] = L², [dv/dy] = T⁻¹. Hence, [η] = [MLT⁻²]/[L²T⁻¹] = ML⁻¹T⁻¹. Its SI unit is N·s/m² which is equal to Pa·s. Correct option: A.