Question

Dimensions of surface tension are:

• A. $\left[M^2{L}^2{T}^{-2}\right]$
• B. $\left[M^{2}L{T}^{-2}\right]$
• C. $\left[M{T}^{-2}\right]$
• D. $\left[ML{T}^{-2}\right]$

Answer 1

Answer: (C)

The surface tension of a liquid is defined as the force per unit length $(F)$ in the plane of the liquid surface, acting at right angles on either side of an imaginary line drawn in the surface.
$T=\frac{F}{l}=\frac{\text{ Newton }}{\text{ metre }}$
$[T]=\frac{\left[ML{T}^{-2}\right]}{[L]}=\left[M{T}^{-2}\right]$
Hence, dimensions of surface tension are $\left[M{L}^{-2}\right]$.
Alternative : Surface tension of a liquid is equal to the work required to increase the surface area of the liquid film by unity at constant temperature.
$\therefore T=\frac{W}{\Delta A}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^2\right]}=\left[M{T}^{-2}\right]$
Hence, dimensions of surface tension are $\left[M{T}^{-2}\right]$