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

Answer

A

Explanation

Let `S= kE^(a)V^(b)T^(c)`
wher k is a dimensionless constant.
Writing the dimensions on both sides we get
`[M^(1)L^(0)T^(-2)]= [ML^(2)T^(-2)]^(a) [LT^(-1)]^(b)[T]^(c)= [M^(a)L^(2a+b)T^(-2a-b+c)]`
Applying principle of homogeneity of dimensions, we get
a= 1 ..(ii)
2a+ b= 0 ....(ii)
-2a-b+c= 0 ....(iii)
Adding (ii) and (iii) we get
c=-2
From (ii) b= -2a =-2
`:. S= kEV^(-2)T^(-2)` or `[S]= [EV^(-2)T^(-2)]`