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

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

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

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

`[E^(-2) V^(-1) T^(-3)]`

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

Text Solution

Verified by Experts

The correct Answer is:

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 )]`
`[M^(1)L^(0)T^(2)] = k [M]^(a) [L]^(2a +b) [T]^(-2a-b+c)`
Comparision
`a =1 " "2a+b=0 " " -2= -2a -b +c`
`" " b=-2 " " -2 = -2(1)+ 2+c`
`" " c =-2`
So the dimensional formula for surface tension will be `[E^(1)V^(-2)T^(-2)]`
Alternate solution :
Surface Tension = `("Surface energy")/("Area")`
[Surface tension] = `([E])/([V. T]^(2)) = [E V^(-2)T^(-2)]`

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The dimension formula for surface tension is :

`[MT^(2)]`

`[ML^(0)T^(-2)]`

`[M^(-1)L^(0) T^(-2)]`

`[ML^(2)T^(-2)]`

If energy E , velocity v and time T are taken as fundamental quanties, the dimensional formula for surface tension is

`[Ev^(-2) T^(-2)]`

`[E^(2) vT^(-2)]`

`[Ev^(-2) T^(-1)]`

`[E^(-2) v^(-2) T^(-1)]`

If force F, Length L and time T are chosen as fundamental quantities , the dimensioal formula for mass is

[FLT]

`[F^(-1) L^(-1) T^(-2)]`

`[F^(-2) L^(-2) T^(-2)]`

`[F^(1) L^(-1) T^(-2)]`