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

The Correct Option is 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.
$T=\frac{F}{l}=\frac{\text { Newton }}{\text { metre }}$
$[T]=\frac{\left[ MLT ^{-2}\right]}{[ L ]}=\left[ MT ^{-2}\right]$
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 $\left[ MT ^{-2}\right]$