A) \[\left[ {{M}^{2}}{{L}^{2}}{{T}^{-2}} \right]\]
B) \[\left[ {{M}^{2}}L{{T}^{-2}} \right]\]
C) \[\left[ M{{T}^{-2}} \right]\]
D) \[\left[ ML{{T}^{-2}} \right]\]
Correct Answer: C
Solution :
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. \[T=\frac{F}{l}=\frac{Newton}{metre}\] \[\left[ T \right]=\frac{\left[ ML{{T}^{-2}} \right]}{\left[ L \right]}=\left[ M{{T}^{-2}} \right]\] 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 \[\left[ M{{T}^{-2}} \right].\]
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