Question

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

Answer 1

`T=f/l,`SI unit is N/m

Its dimensions `= ([L^1M^1T^-2])/([L^1M^0T^0])`

`=[L^0M^1T^-2]       ...(1)`

Also, `T = (dW)/(dA),` SI unit is J/m²

Its dimensions, `=(dW)/(dA)=("Force"xx"displacement")/"Area"`

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

`=[L^0M^1T^-2]     ...(2)`

From (1) and (2)

`T= f/l=W/A`

SI unit of surface tension i.e. N/m and J/m² are equivalent.