Question

Prove that, equivalent S.I. unit of surface tension is J/m².

Answer 1

T = `F/L`

where F = Force (N), L = Length (m)

= SI unit of T = `N/m`

Surface tension can also be written as

T = `W/A`

where W = Work (J), A = Area (m²)

= SI unit of T = `J/m^2`

We know

1J=1N×1m

So,

`J/m^2 = (N * m)/m^2 = N/m`

Both units are the same

`1N/m equiv 1J/m^2`