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JEE Main 2021 (26 Aug, Shift 1) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2021 (26 Aug, Shift 1)

Q45JEE Main 2021 · 26 AUG · SHIFT 1Medium

Applications of Dimensional Analysis

If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula P = EL2M $-5\mathrm{G}-$ 2 are:

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Answer: (d)

$[E] = ML^2T^{-2}$ , $[L^2] = M^2L^4T^{-2}$ , $[M^{-5}] = M^{-5}$ , $[G^{-2}] = M^{2}L^{-6}T^{4}$ .
Powers of M: $1 + 2 - 5 + 2 = 0$ ; L: $2 + 4 - 6 = 0$ ; T: $-2 - 2 + 4 = 0$ .
So $P$ is dimensionless: the answer is (d) $[M^0L^0T^0]$ .

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