If energy (E),velocity (V),and time (T) are c | vedclass

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(C) Let the dimensional formula of surface tension $(S)$ be $S = E^x V^y T^z$.The dimensions of surface tension are $[S] = [MT^{-2}]$.The dimensions o

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$[EV^{-2}T^{-2}]$

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(C) Let the dimensional formula of surface tension $(S)$ be $S = E^x V^y T^z$.The dimensions of surface tension are $[S] = [MT^{-2}]$.The dimensions of the fundamental quantities are:$[E] = [ML^2T^{-2}]$$[V] = [LT^{-1}]$$[T] = [T]$Substituting these into the equation:$[MT^{-2}] = [ML^2T^{-2}]^x [LT^{-1}]^y [T]^z$$[MT^{-2}] = [M^x L^{2x+y} T^{-2x-y+z}]$Comparing the powers of $M, L,$ and $T$ on both sides:For $M$: $x = 1$For $L$: $2x + y = 0 \Rightarrow 2(1) + y = 0 \Rightarrow y = -2$For $T$: $-2x - y + z = -2 \Rightarrow -2(1) - (-2) + z = -2 \Rightarrow -2 + 2 + z = -2 \Rightarrow z = -2$Thus,the dimensional formula is $[EV^{-2}T^{-2}]$.

If energy $(E)$,velocity $(V)$,and time $(T)$ are chosen as the fundamental quantities,the dimensional formula of surface tension will be

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