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Which one of the following represents the correct dimensions of the coefficient of viscosity?

Asked in AIEEE 2004 · Dimensional formula of a named quantity

(1) [ML⁻¹T⁻²]
(2) [MLT⁻¹]
(3) [ML⁻¹T⁻¹]
(4) [ML⁻²T⁻²]

Answer: (3) [ML⁻¹T⁻¹]

Step-by-step solution

Idea: viscosity comes from F=η A(dv)/(dx).

Rearranging: η=F/(A (dv/dx)).

=([MLT⁻²])/([L²][T⁻¹]).

=[ML⁻¹T⁻¹].

Why the other options are wrong

(1) comes from is a pressure
(2) comes from carries the length exponent with the wrong sign
(4) comes from is a pressure gradient

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