Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsMechanical Properties of Fluids3 Marks
Question
Obtain the dimensions of surface tension.
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Answer
Surface tension is a force per unit length. $\therefore$ [Surface tension] $=$ $ \frac{\text { [force }]}{\text { length }]}=\frac{\left[\mathrm{ML}^1 \mathrm{~T}^{-2}\right]}{\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^0\right]}=\left[\mathrm{ML}^0 \mathrm{~T}^{-2}\right] \quad O R $ Surface tension is also equal to the surface energy per unit surface area of a liquid. $ \begin{aligned} &\therefore \text { [Surface tension }]=\frac{\text { [energy }]}{\text { [area] }}=\frac{[\text { work }]}{\text { [area }]} \\ &=\frac{[\text { force }] \text { [displacement }]}{[\text { area] }} \\ &=\frac{\left[\mathrm{ML}^1 \mathrm{~T}^{-2}\right]\left[\mathrm{M}^0 \mathrm{~L}^1 \mathrm{~T}^0\right]}{\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^0\right]}=\left[\mathrm{ML}^0 \mathrm{~T}^{-2}\right] \end{aligned} $
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