If momentum (P),area (A),and time (T) are tak | vedclass

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(B) Let energy $E$ be expressed as $E = k P^x A^y T^z$,where $k$ is a dimensionless constant.Dimensional formula of energy $[E] = [M^1 L^2 T^{-2}]$.Di

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$P^1 A^{1/2} T^{-1}$

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(B) Let energy $E$ be expressed as $E = k P^x A^y T^z$,where $k$ is a dimensionless constant.Dimensional formula of energy $[E] = [M^1 L^2 T^{-2}]$.Dimensional formula of momentum $[P] = [M^1 L^1 T^{-1}]$.Dimensional formula of area $[A] = [L^2]$.Dimensional formula of time $[T] = [T^1]$.Substituting these into the equation:$[M^1 L^2 T^{-2}] = [M^1 L^1 T^{-1}]^x [L^2]^y [T^1]^z$$[M^1 L^2 T^{-2}] = [M^x L^{x+2y} T^{-x+z}]$Comparing the powers of $M$,$L$,and $T$ on both sides:For $M$: $x = 1$For $L$: $x + 2y = 2$For $T$: $-x + z = -2$Substituting $x = 1$ into the $L$ equation: $1 + 2y = 2 \implies 2y = 1 \implies y = 1/2$.Substituting $x = 1$ into the $T$ equation: $-1 + z = -2 \implies z = -1$.Thus,the dimensional formula for energy is $[P^1 A^{1/2} T^{-1}]$.

If momentum $(P)$,area $(A)$,and time $(T)$ are taken to be fundamental quantities,then energy has the dimensional formula of:

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