The energy(E), velocity (V)and time(T)are chosen as fundamental quantities , dimensional formula of surface tension is?

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Answer

Answer

Answer

Dimensional formula of surface tension:

Surface tension is defined as the force acting per unit length perpendicular to an imaginary line drawn on the surface of a liquid. It is denoted by the symbol ‘γ’ and its unit is N/m or J/m².

The dimensional formula of surface tension can be derived using the principle of homogeneity of dimensions. According to this principle, the dimensions of the physical quantity on the left-hand side of an equation must be equal to the dimensions of the physical quantity on the right-hand side of the equation.

Derivation:

The formula for surface tension is given by:

γ = F/L

Where F is the force acting perpendicular to the surface of the liquid and L is the length of the imaginary line on the surface of the liquid.

The dimensional formula of force is [M L T^-2] and the dimensional formula of length is [L]. Therefore, the dimensional formula of surface tension can be derived as follows:

γ = F/L

[M L T^-2]/[L]

[M T^-2]

Therefore, the dimensional formula of surface tension is [M T^-2].

Conclusion:

Surface tension is a physical quantity that is dimensionally represented by the formula [M T^-2]. It is a fundamental property of liquids that arises due to the cohesive forces between the molecules of the liquid. The dimensional analysis of surface tension helps us to understand the relationship between the fundamental units of energy, velocity, and time in terms of this physical quantity.

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