If energy ( E), velocity ( V) and time (...

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

`EV^(-2)T^(-1)`

`EV^(-1)T^(-2)`

`EV^(-2)T^(-2)`

`EV^(-2)T^(-3)`

Text Solution

Verified by Experts

The correct Answer is:

Dimension of mass,
`[M] = ML^(2) T^(-2).L^(-2)T^(2)= ML^(2)T^(-2).(LT^(-1))^(-2)=EV^(-2)`
Therefore dimensional formula of surface tension,
`MT^(-2) = EV^(-2)T^(-2)`

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If force (F) ,velocity(V) and time (T) are taken as fundamental units,then the dimensions of mass are

`[FVT^-1]`

`[FVT^-2]`

`[FV^-1T^-1]`

`[FV^-1T]`

If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then energy has the dimensional formula

`[P^1A^-1T^-1]`

`[P^2A^1T^1]`

`[P^1A(1//2)T^-1]`

`[P^2^1T^1]`

In energy (E), momentum (P) and frozen (F) are chosen as fundamental units. The dimensions of mass in new system is

`E^-1 P^3`

`E^-1 P^2`

`E^-2 P^2`

None of these