Question

If energy $\left(E\right)$, velocity $\left(v\right)$ and time $\left(T\right)$ are fundamental units. What will be the dimension of surface tension?

• A. $\left[S\right]=E{v}^{-2}{T}^{-2}$
• B. $\left[S\right]=E{v}^{-1}{T}^{-2}$
• C. $\left[S\right]=E{v}^{-2}{T}^{-1}$
• D. None of these

Answer 1

Answer: (A)

$\left[S\right]=E{v}^{-2}{T}^{-2}$

Surface tension $\left(S\right)$$=\frac{workdone}{Area}=\frac{Energy}{Area}=\left[\begin{array}{c}\frac{E}{A}\end{array}\right]=\left[\begin{array}{c}\frac{E}{L^2}\end{array}\right]$

$\because L=vT\therefore S=\frac{E}{(vT{)}^2}=E{v}^{-2}{T}^{-2}$