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JEE Main 2023 (13 Apr, Shift 2) · Applications of Dimensional Analysis

Applications of Dimensional Analysis question from JEE Main 2023 (13 Apr, Shift 2)

Q26JEE Main 2023 · 13 APR · SHIFT 2Easy

Applications of Dimensional Analysis

In the equation $\left[X + \frac{a}{Y^2}\right][Y - b] = \mathrm{R}T, X$ is pressure, $Y$ is volume, $\mathrm{R}$ is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is:

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Answer: (b)

$[a] = [X][Y^2]$ (pressure $\times$ volume $^2$ ), $[b] = [Y]$ (volume).
$[a/b] =$ pressure $\times$ volume $= [ML^2T^{-2}]$ .
So the answer is (b) energy.

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