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JEE Main 2023 (15 Apr, Shift 1) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2023 (15 Apr, Shift 1)

Q32JEE Main 2023 · 15 APR · SHIFT 1Medium

Applications of Dimensional Analysis

The speed of a wave produced in water is given by $v = \lambda^{a}g^{b}\rho^{c}$ . Where $\lambda, g$ and $\rho$ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of $a, b$ and $c$ respectively, are:

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Answer: (d)

$LT^{-1} = L^a\,(LT^{-2})^b\,(ML^{-3})^c$ .
M: $c = 0$ ; T: $-2b = -1 \Rightarrow b = \frac{1}{2}$ ; L: $a + b - 3c = 1 \Rightarrow a = \frac{1}{2}$ .
So the answer is (d) $\frac{1}{2}, \frac{1}{2}, 0$ .

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