Question

The dimensions of surface tension are
A. $M{{L}^{-1}}{{T}^{-2}}$
B. $ML{{T}^{-2}}$
C. $M{{L}^{-1}}{{T}^{-1}}$
D. $M{{T}^{-2}}$

Answer 1

You could begin from the very definition of surface tension. You may recall that it is the force acting per unit length. Now you could break down the derived quantities into the fundamental quantities to make it easy for us to find their respective dimensions and then substitute to get the answer.

Complete step by step solution:
In the question, we are asked to find out which among the given set of dimensions correctly represents the dimension of surface tension. In order to answer the question you should have knowledge of what surface tension is.
Surface tension can be defined as that property of the liquid surface by virtue of which it resists an external force which happens due to the cohesive nature of its molecules.
Let S be the surface tension of a liquid surface, F be the force and L be the length at which this force is acting then, surface tension is given by,
$S=\dfrac{F}{L}$
Where,
$F=ma$ from Newton’s second law.
Also,
$a=\dfrac{v}{t}$
$\Rightarrow S=\dfrac{mv}{Lt}$
Now substituting the dimensions of each of these physical quantities we have,
$\left[ S \right]=\dfrac{\left[ M \right]\left[ L{{T}^{-1}} \right]}{\left[ L \right]\left[ T \right]}$
$\therefore \left[ S \right]=\left[ M{{T}^{-2}} \right]$
Therefore, we found that the dimension of surface tension is given by$M{{T}^{-2}}$. Hence, option D is the correct option.

Note: You should remember that doing dimensional analysis doesn’t give us the constants that are present. That is, a dimensionally correct equation may not always be the real equation due to the same reason. Here, we are basically expressing the derived quantities in terms of fundamental quantities raised to some power.