Let the dimensional formula of surface tension ($S$) be related to energy ($E$), velocity ($v$), and time ($T$) as: $[S] = E^a v^b T^c$ Substituting the dimensions of each quantity: Dimension of surface tension, $S = \frac{\text{Force}}{\text{Length}} = \frac{[M L T^{-2}]}{[L]} = [M L^0 T^{-2}]$ Dimension of energy, $E = [M L^2 T^{-2}]$ Dimension of velocity, $v = [L T^{-1}]$ Dimension of time, $T = [T]$

$[M^1 L^0 T^{-2}] = [M L^2 T^{-2}]^a [L T^{-1}]^b [T]^c$ $[M^1 L^0 T^{-2}] = [M^a L^{2a+b} T^{-2a-b+c}]$ Equating the powers of $M$, $L$, and $T$ on both sides, we get: For $M$: $a = 1$ For $L$: $2a + b = 0 \implies 2(1) + b = 0 \implies b = -2$ For $T$: $-2a - b + c = -2 \implies -2(1) - (-2) + c = -2 \implies -2 + 2 + c = -2 \implies c = -2$

Therefore, the dimensional formula for surface tension is $[E^1 v^{-2} T^{-2}]$ or $[E v^{-2} T^{-2}]$.