c
\(S = E ^{ x } V ^{ y } T ^{ z }\)

\(S = \frac FL\) \(\Rightarrow[ T ]=\left[ MT ^{-2}\right]\)

\([ E ]=\left[ ML ^2 T ^{-2}\right]\)

\({[ V ]=\left[ LT ^{-1}\right] }\)

\({[ T ]=[ T ] }\)

\({\left[ MT { }^{-2}\right]=\left[ E ^{ x } V ^{ y } t ^{ z }\right]=\left[ ML ^2 T ^{-2}\right]^{ x }\left[ LT ^{-1}\right]^{ y }[ T ]^{ z } }\)

Comparing coefficients

\(x=1\)

\(2 x+y=0\)

\(-2 x-y+z=-2\)

Solving above equations \(x =1, y =-2, z =-2\)

Substituting in expression of surface tension:

\(S = EV ^{-2} T ^{-2}\)