Q 11-01-097JEE MainJEE Main 2024 (5 Apr, Shift 2)Medium
What is the dimensional formula of $ab^{-1}$ in the equation $\left(P + \dfrac{a}{V^2}\right)(V - b) = RT$, where the letters have their usual meaning?
Answer: (C) $[\text{M}\text{L}^2\text{T}^{-2}]$
$\dfrac{a}{V^2}$ has the dimensions of pressure: $[a] = [\text{M}\text{L}^{-1}\text{T}^{-2}][\text{L}^6] = [\text{M}\text{L}^5\text{T}^{-2}]$.
$b$ has the dimensions of volume: $[b] = [\text{L}^3]$.
$$\left[\frac ab\right] = [\text{M}\text{L}^2\text{T}^{-2}]$$
Solution by Sreeraj P, M.Sc Physics