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)

$\left[ M{{T}^{-2}} \right]$

Answer 2

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.
$T=\frac{F}{l}=\frac{\text { Newton }}{\text { metre }}$
$[T]=\frac{\left[ MLT ^{-2}\right]}{[ L ]}=\left[ MT ^{-2}\right]$
Hence, dimensions of surface tension are $\left[ ML ^{-2}\right]$.
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.
$\therefore T=\frac{W}{\Delta A}=\frac{\left[M L^{2} T^{-2}\right]}{\left[L^{2}\right]}=\left[ MT ^{-2}\right]$
Hence, dimensions of surface tension are $\left[ MT ^{-2}\right]$