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)]`

Answer

B

Explanation

Let surface tension
`sigma =E^(a)V^(b) T^c`
equating the dimension of LHS and RHS
`(M^1L^1T^(-2))/L=(M^1L^2T^(-2))^(a) (L/T)^(b) (T)^c`
`M^(1)L^(0) T^(-2)=M^(a) L^(2a+b) T^(2a-b+c)`
`impliesa = 1, 2a + b = 0, - 2a - b + c = -2`
`sigma =E^(1) V^(-2) T^(-2)`