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JEE Main 2022 (26 Jun, Shift 1) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2022 (26 Jun, Shift 1)

Q39JEE Main 2022 · 26 JUN · SHIFT 1Medium

Applications of Dimensional Analysis

An expression for a dimensionless quantity P is given by $P = \frac{\alpha}{\beta}\log_e\left(\frac{kt}{\beta x}\right)$ ; where $\alpha$ and $\beta$ are constants, x is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of $\alpha$ will be:

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Answer: (c)

The log argument is dimensionless: $[\beta x] = [kt] =$ energy, so $[\beta] = \dfrac{ML^2T^{-2}}{L} = MLT^{-2}$ .
$P$ and the log are dimensionless, so $[\alpha] = [\beta]$ .
$[\alpha] = [MLT^{-2}]$ , so the answer is (c).

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