Question

If energy (E),velocity (V) and time (T) are chosen as the fundamental quantities, then the dimensions of surface tension will be. (Surface tension=force/length)
(A) `EV^(-2)T^(-1) " " (B) EV^(-1)T^(-3) " " (C)E^(-2)V^(-1)T^(-3) " " (D)EV^(-2)T^(-2)`

Answer 1

[surface tension]=[force/length] `=M^(1)L^(0)T^(-2)`
suppose [surface tension] `=E^(a)V^(b)T^(c)`
`:.M^(1)L^(0)T^(-2)=[M^(1)L^(2)T^(-2)]^(a)[L^(1)T^(-1)]^(b)[T]^(c)`
Matching dimensions of M `rArr a=1`
Matching dimensions of `L rArr2a+b=0rArrb=-2`
Matching dimensions of `TrArr-2a-b+c=-2rArrc=-2`
`:.` [surface tension] `=EV^(-2)T^(-2)`