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 `S prop E^a upsilon^b T^c , S = kE^a upsilon^b T^c …. (i)`
`:. M^1 L^0 T^(-2) = k [M^1 L^2 T^(-2)]^a [L^1 T^(-1)]^b [T]^c`
or `M^1 L^0 T^(-2) =k M^a L^(2a) T^(-2a) L^b T^(-b) T^c`
or `M^1 L^0 T^(-2) =k M^a L^(-2a +b) T^(-2a - b+c)`
Equating powers of M, L and T, we get `:. a= 1
2a + b =0, b=-2 a = -2
b= -2
or -2a - b + c= -2 , -2(1) - (-2) + c = -2
c =-2
`"Putting values"` of a, b and c in (i)
`S = k E^1 upsilon^(-2) T^(-2)`