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

Options

A. `[EV^(-1) T^(-2)]`
B. `[EV^(-2) T^(-2)]`
C. `[E^(-2) V^(-1) T^(-3)]`
D. `[EV^(-2) T^(-1)]`

Explanation

Surface tension `S = fn (E, V, T)`
`S prop E^(a) V^(b) T^(C )`
`M^(1) L^(0) ^(-2) prop [ ML^(2) T^(-2)]^(-2) [LT^(-1)]^(b) [T]^(c )`
`prop M^(a) L^(a) L^(2a + b) T^(-2a - b + c)`
Comparing powers of `M, L` and `T`
`M : a = 1`
`L : 2a + b = 0 implies b = - 2a = - 2`
`T : - 2a - b + c = - 2`
`- 2 + 2 + c = - 2 implies c = - 2`
`a = 1, b = - 2, c = - 2`
`S prop EV^(2) T^(-2)`