Question

The dimensions of surface tension are:

Answer 1

Hint: In this question, we will first study the basic definition of surface tension and the S.I unit of surface tension, this will help us to get the dimensional formula for surface tension. Further, we will study the basics of force, for our better understanding.
Formula used:
$\gamma = \dfrac{1}{2}\dfrac{F}{L}$

Complete answer:
As we know that surface tension can be defined as the force per unit length which is perpendicular to a line drawn in the surface of the liquid. The S.I unit of surface tension is given by Newton per meter, and in C.G.S unit surface tension is given as dynes per centimeter.
We can write the expression of surface tension as:
$\gamma = \dfrac{1}{2}\dfrac{F}{L}$
Here, F is the force applied on the object and L is the length.
As we know the unit of force is Newton, and unit of force is meter, so, the dimensional formula will be:
$\left[ {{M^1}{L^0}{T^{ - 2}}} \right]$, which can be written as: $\left[ {M{T^{ - 2}}} \right]$.
Here, M is mass, L is length and T is the time.
Therefore, we get the required answer.

Additional information:
We know that force is simply any push or pull. The S.I unit of force is Newton which is represented by N. Force is given by product of mass and acceleration. Here acceleration is defined as the increase in the velocity of an object. The acceleration is measured in meters per Second Square.
As we know that there are three laws of motions given by Newton. These laws of motion relate an object's motion to the forces acting on it.
First law of motion states that an object continues to be in rest or in motion in a particular direction until and unless any external force is applied on it.
Now in the second law of motion, the force on an object is equal to its mass times its acceleration. This law also gives the relation of momentum and force.
The last one is the third law of motion, every action has an equal and opposite reaction.

Note:
We should remember that the cohesive forces experienced between liquid molecules are responsible for the phenomenon called surface tension. We should also note that we can answer this question by knowing the basic definition and unit of surface tension.