Question

If momentum (P), area (A), and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is .

Answer 1

1. Dimension of energy $\left(E\right)$ = $M{L}^2{T}^{-2}$………..$\left(1\right)$
2. Dimension of momentum $\left(P\right)$ = $ML{T}^{-1}$……..$\left(2\right)$
3. Dimension of area $\left(A\right)$ = $L^2$ or $A^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$………….$\left(3\right)$
4. Substituting equation $\left(2\right)and\left(3\right)inequation\left(1\right)$, we get
5. Dimensional formula for energy $\left(E\right)$ = $P^1{T}^{-1}{A}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

Thus, the dimensional formula for energy = $P{T}^{-1}{A}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$