| We know that |
| Surface tension (S)=$\frac{Force[F]}{Lenght[L]}$ |
| So, [S] = $\frac{[MLT^{-2}]}{L}$ |
| Energy (E) = Force *displacement |
| [E] = [M$LT^{-2}$][L]} = [M$L^{2}T^{-2}$] |
| Velocity [V] = [L$T^{-1}$] |
| |
| Since S ∝ $E^av^bT^c$ |
| where, a, b, c are constants. |
| From the principle of homogeneity, |
| Dimension of [LHS] = Dimension of [RHS] |
| $[ML^0T^{-2}]$ = $[ML^{2}T^{-2}]^a[LT^{-1}]^b [T]^c$ |
| =[$M^aL^{2a+b}T^{-2a-b+c}$] |
| Equating the power on both sides, we get |
|
a=1 , 2a+b=0 ⇒ b=-2
-2a-b+c= -2 ⇒ c = -2
So [S] = [E$V^{-2}T^{-2}$]
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