Physics - Unit & Dimension Question with Solution | TestHub

$X \& \frac{a}{Y^2}$ have the same dimensions. $Y \& b$ also have the same dimensions.

Therefore,

$$\begin{gathered} \frac{a}{Y^2}=M{L}^{-1}{T}^{-2} \\ \Rightarrow a=M{L}^{-1}{T}^{-2}\times L^6=M{L}^5{T}^{-2} \end{gathered}$$

and $b=L^3$.

So, the dimensions of $\frac{a}{b}$ is,

$\frac{a}{b}=\frac{M{L}^5{T}^{-2}}{L^3}=M{L}^2{T}^{-2}$.

This is the dimensional form of energy. Hence, this is the right option.