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JEE Main 2022 (25 Jul, Shift 1) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2022 (25 Jul, Shift 1)

Q36JEE Main 2022 · 25 JUL · SHIFT 1Easy

Applications of Dimensional Analysis

If momentum [P], area $[\mathrm{A}]$ and time $[\mathrm{T}]$ are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is:

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Answer: (a)

$\eta = \dfrac{F/A}{dv/dx}$ , and velocity gradient has dimensions $[T^{-1}]$ .
$[\eta] = [F][A^{-1}][T]$ , with force $F = P/T$ .
$[\eta] = [PT^{-1}][A^{-1}][T] = [PA^{-1}T^0]$ .
So the answer is (a).

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