Q 11-01-185JEE MainJEE Main 2021 (26 Feb, Shift 2)Medium
If $C$ and $V$ represent capacity and voltage respectively then what are the dimensions of $\lambda$ where $C/V = \lambda$?
Answer: (A) $[\text{M}^{-2}\text{L}^{-4}\text{I}^3\text{T}^7]$
$[V] = \dfrac{[\text{work}]}{[\text{charge}]} = \dfrac{\text{ML}^2\text{T}^{-2}}{\text{IT}} = [\text{ML}^2\text{T}^{-3}\text{I}^{-1}]$
$[C] = \dfrac{[Q]}{[V]} = [\text{M}^{-1}\text{L}^{-2}\text{T}^4\text{I}^2]$
$$[\lambda] = \frac{[C]}{[V]} = [\text{M}^{-2}\text{L}^{-4}\text{I}^3\text{T}^7]$$
Solution by Sreeraj P, M.Sc Physics