If energy `E`, velocity `v` and time `T` are taken as fundamental quanties, the dimensional formula for surface tension is

Options

A. `[Ev^(-2) T^(-2)]`
B. `[E^(2) vT^(-2)]`
C. `[Ev^(-2) T^(-1)]`
D. `[E^(-2) v^(-2) T^(-1)]`

Answer

A

Explanation

`[S] prop [E]^(a) xx [v]^(b) xx [T]^(c)`
`[MT^(-2)] = [ML^(2)T^(-2)] xx [LT^(-1)]^(b) xx [T]^(c)`
Comparing the powers on both sides we get a,b,c