An equation is given here (P + a/V²) = b(θ)/(V) where P = Pressure, V = Volume and θ = Absolute temperature. If a and b are constants, the dimensions of a will be (a) [ML⁻⁵T⁻¹] (b) [ML⁵T¹] (c) [ML⁵T⁻²] (d) [M⁻¹L⁵T²]

Answer: (c). a/V² is added to P, so it has dimensions of pressure. [a] = [P][V²] = [ML⁻¹T⁻²][L⁶] = [ML⁵T⁻²]. So the answer is (c).

An equation is given here (P + a/V²) = b(θ)/(V) where P = Pressure, V… | NEET 1996 (AIPMT)

Q80NEET 1996 · AIPMTEasy

Applications of Dimensional Analysis

An equation is given here $\left(P + \frac{a}{V^2}\right) = b\frac{\theta}{V}$ where $P$ = Pressure, $V$ = Volume and $\theta$ = Absolute temperature. If $a$ and $b$ are constants, the dimensions of $a$ will be

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Answer: (c)

$a/V^2$ is added to $P$ , so it has dimensions of pressure.
$[a] = [P][V^2] = [ML^{-1}T^{-2}][L^6] = [ML^5T^{-2}]$ .
So the answer is (c).

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Applications of Dimensional Analysis question from NEET 1996 (AIPMT)

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