If energy ( E ) , velocity ( V ) and time ( T ) are chosen as the...

Dimensional formula of surface tension, $\left[S\right] = \left[{M}^{1}{L}^{0}{T}^{- 2}\right]<br />Dimensional formula$ of $energy, \left[E\right] = \left[{M}^{1}{L}^{2}{T}^{- 2}\right]<br />Dimensional formula of velocity, \left[V\right] = \left[{M}^{0}{L}^{1}{T}^{- 1}\right]<br /><br />By applying dimensional analysis,<br />$S = {E}^{a}{V}^{b}{T}^{c}$<br />\left[{M}^{1}{L}^{0}{T}^{- 2}\right] = {\left[{M}^{1}{L}^{2}{T}^{- 2}\right]}^{a}{\left[{M}^{0}{L}^{1}{T}^{- 1}\right]}^{b}{\left[T\right]}^{c}$
\left[{M}^{1}{L}^{0}{T}^{- 2}\right] = {M}^{a}{L}^{2a + b}{T}^{- 2a - b + c}$<br /><br />On comparing,<br />$a = 1$<br />$2a + b = 0 ⇒ b = - 2$<br />$- 2a - b + c = - 2 ⇒ c = - 2$<br />$∴ S = {E}^{1}{V}^{- 2}{T}^{- 2}