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

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(B) Let the dimensional formula for energy be $[E] = [P]^x [A]^y [T]^z$. Substituting the dimensions of each quantity: $[M L^2 T^{-2}] = [M L T^{-1}]^

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

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(B) Let the dimensional formula for energy be $[E] = [P]^x [A]^y [T]^z$. Substituting the dimensions of each quantity: $[M L^2 T^{-2}] = [M L T^{-1}]^x [L^2]^y [T]^z$. Equating the powers of $M, L,$ and $T$ on both sides: $M^1 L^2 T^{-2} = M^x L^{x+2y} T^{-x+z}$. Comparing the exponents: For $M$: $x = 1$. For $L$: $x + 2y = 2$. Substituting $x=1$,we get $1 + 2y = 2$,which implies $2y = 1$,so $y = 1/2$. For $T$: $-x + z = -2$. Substituting $x=1$,we get $-1 + z = -2$,which implies $z = -1$. Thus,the dimensional formula for energy is $[P^1 A^{1/2} T^{-1}]$ or $[P A^{1/2} T^{-1}]$.

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

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