Q 11-01-124JEE MainJEE Main 2024 (31 Jan, Shift 2)Medium
Consider two physical quantities $A$ and $B$ related to each other as $E = \dfrac{B - x^2}{At}$, where $E$, $x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $AB$ is
Answer: (B) $\mathrm{L^2M^{-1}T^1}$
$B$ is subtracted from $x^2$, so $[B] = \mathrm{L^2}$.
$[A] = \dfrac{[B]}{[E][t]} = \dfrac{\mathrm{L^2}}{\mathrm{ML^2T^{-2}}\cdot\mathrm T} = \mathrm{M^{-1}T}$.
$[AB] = \mathrm{L^2M^{-1}T^1}$.
Solution by Sreeraj P, M.Sc Physics