Question

If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is ______.

Options

• [P A^-1 T⁰]

• [P A T^-1]

• [P A^-1 T]

• [P A^-1 T^-1]

Answer 1

If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is [P A^-1 T⁰].

Explanation:

F = η A `"dV"/"dx"` ⇒ η = `"Fdx"/"A dV"` 

⇒ [η] = `(["F"]["dx"])/(["A"]["dV"])= (["F"]["d t"]["dx"])/(["A"]["d t"]["dV"])`

= `(["P"]["dx"])/(["A"]["dx"])`

= [P A^-1 T⁰]