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JEE Main 2021 (27 Aug, Shift 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2021 (27 Aug, Shift 2)

Q43JEE Main 2021 · 27 AUG · SHIFT 2Easy

Applications of Dimensional Analysis

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density:

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Answer: (a)

From $F = ma$ : $[M] = [F][a]^{-1} = F\,L^{-1}T^{2}$ .
Density $\rho = \dfrac{M}{L^3} = F\,L^{-1}T^{2}\cdot L^{-3}$ .
$[\rho] = [FL^{-4}T^{2}]$ , so the answer is (a).

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