Question 2

Consider two physical quantities $$A$$ and $$B$$ related to each other as $$E = \frac{B - x^2}{At}$$ where $$E$$, $$x$$ and $$t$$ have dimensions of energy, length and time respectively. The dimension of $$AB$$ is

$$E=\frac{B-x^2}{At}$$. $$[B]=[x^2]=L^2$$. $$[A]=[B]/([E][t])=L^2/(ML^2T^{-2}\cdot T)=L^2/(ML^2T^{-1})=M^{-1}T$$.

$$[AB]=M^{-1}T\cdot L^2=L^2M^{-1}T^1$$.

The answer is Option (2): $$L^2M^{-1}T^1$$.

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