If energy(E), velocity(V) and time(T) are chosen as fundamental quantities, the dimensional formula of surface tension will be

Options

(a) EV⁻¹T⁻²
(b) EV⁻²T⁻²
(c) E⁻²V⁻¹T⁻³
(d) EV⁻²T⁻¹

Correct Answer:

EV⁻²T⁻²

Explanation:

Let surface tension s = EᵃVᵇTᶜ
MLT⁻² / L = (ML²T⁻²)ᵃ (L / T)ᵇ (T)ᶜ
Equating the dimension of LHS and RHS
ML⁰T⁻² = MᵃL²ᵃ⁺ᵇT⁻²ᵃ⁻ᵇ⁺ᶜ
⇒ a = 1, 2a + b = 0, -2a -b + c = -2
⇒ a = 1, b = -2, c = -2
Hence, the dimensions of surface tension are [EV⁻²T⁻²].