What is the dimensional formula of a b^{-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.

Q: What is the dimensional formula of $a b^{-1}$ 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.

b $\because[\mathrm{V}]=[\mathrm{b}]$ $\therefore \text { Dimension of } \mathrm{b}=\left[\mathrm{L}^3\right]$ $\&[\mathrm{P}]=\left[\frac{\mathrm{a}}{\mathrm{V}^2}\right]$ ${[\mathrm{a}]=\left[\mathrm{PV}^2\right]=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\left[\mathrm{L}^6\right]}$ $\text { Dimension of } \mathrm{a}=\left[\mathrm{ML}^5 \mathrm{~T}^{-2}\right]$ $\therefore \mathrm{ab}^{-1}=\frac{\left[\mathrm{ML}^5 \mathrm{~T}^{-2}\right]}{\left[\mathrm{L}^3\right]}=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

What is the dimensional formula of $a b^{-1}$ 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.

A$\left[\mathrm{M}^6 \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$
B$\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]$
C$\left[M^{-1} L^j T^3\right]$
D$\left[M^6 L^7 T^4\right]$

JEE MAIN 2024, Diffcult

STD 11 Science
JEE
STD 11 - 1. units,dimensions and measurement
Physics

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