What is the dimensional formula of ab⁻¹ in the equation (P + a/V²)(V - b) = RT, where letters have their usual meaning. (a) [M⁶L⁷T⁴] (b) [M⁻¹L⁵T³] (c) [M⁰L³T⁻²] (d) [ML²T⁻²]

Answer: (d). [a] = [P][V²] = [ML⁻¹T⁻²][L⁶] = [ML⁵T⁻²]; [b] = [V] = [L³]. [ab⁻¹] = [ML⁵T⁻²]/[L³] = [ML²T⁻²]. So the answer is (d).

What is the dimensional formula of ab⁻¹ in the equation (P + a/V²)(V… | JEE Main 2024 (5 Apr, Shift 2)

Q19JEE Main 2024 · 5 APR · SHIFT 2Easy

Applications of Dimensional Analysis

What is the dimensional formula of $ab^{-1}$ in the equation $\left(\mathrm{P} + \frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V} - \mathrm{b}) = \mathrm{RT}$ , where letters have their usual meaning.

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Answer: (d)

$[a] = [P][V^2] = [ML^{-1}T^{-2}][L^6] = [ML^5T^{-2}]$ ; $[b] = [V] = [L^3]$ .
$[ab^{-1}] = [ML^5T^{-2}]/[L^3] = [ML^2T^{-2}]$ .
So the answer is (d).

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