Q 11-01-029NEETEAMCET 2009 (Medical)Hard
If energy $E$, velocity $v$ and time $T$ are taken as fundamental quantities, the dimensional formula for surface tension is
Answer: (A) $[Ev^{-2}T^{-2}]$
Surface tension is force per unit length: $[S] = [MT^{-2}]$.
Let $S = E^a v^b T^c$:
$$[MT^{-2}] = [ML^2T^{-2}]^a\,[LT^{-1}]^b\,[T]^c$$
M: $a = 1$
L: $2a + b = 0 \Rightarrow b = -2$
T: $-2a - b + c = -2 \Rightarrow -2 + 2 + c = -2 \Rightarrow c = -2$
So $[S] = [Ev^{-2}T^{-2}]$.
Solution by Sreeraj P, M.Sc Physics