Question

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

Answer 1

Correct Answer - D
[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 dimension of `MrArr a =1`
Matching dimensions of `LrArr 2a+b=0rArr b`
=-2
Matching dimensions of `TrArr -2a-b+crArrc`
=-2
`:.` [sufrace tension]=`EV^(-2)T^(-2)`