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

Options

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

Explanation

Applying dimensional analysis
`S prop E^(a)V^(b)T^(c)`
`M^(1)L^(0)T^(-2)=k[M^(1)L^(2)T^(-2)]^(a)[L^(1)T^(-1)]^(b)[T^(1)]^(c)`
`M^(1)L^(0)T^(-2)=k[M^(a)L^(2a)T^(-2a)]L^(b)T^(-b)T^(c)`
Comparison
`..........`
`c=-2`
So the dimensional formula for surface tension will be `[E^(1)V^(-1)V^(-2)]`
Alternate solution :
Surface tension `=("Surface energy")/("Area")`
[Surface tension] `=([E])/([VT]^(2))=[EV^(-2)T^(-2)]`