Dimensional Formula of Surface Tension

In Class 11 Physics (Units and Measurements), calculating the dimensional formula of various physical quantities is a core skill. Here is the step-by-step derivation for Surface Tension.

Question (Click to Flip)

Does surface tension have the same dimensions as spring constant?

Answer

Yes! The spring constant (k = Force / Extension) is also Force divided by Length. Therefore, the spring constant and surface tension have the exact same dimensional formula: [M¹ L⁰ T⁻²].

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Key Facts

Surface tension is the exact physical phenomenon that allows small insects (like water striders) to walk on water without sinking, as the water's surface acts like a stretched elastic membrane.

Definition and Basic Formula

Surface Tension (T or S) is defined as the force acting per unit length of an imaginary line drawn on the surface of a liquid.

Formula: Surface Tension = Force / Length

Step-by-Step Derivation

To find the dimensional formula, we substitute the basic dimensions of Force and Length.

Dimension of Force (F): Force = Mass × Acceleration [F] = [M¹ L¹ T⁻²]
Dimension of Length (L): [L] = [L¹]
Putting it into the Surface Tension Formula: [Surface Tension] = [F] / [L] [Surface Tension] = [M¹ L¹ T⁻²] / [L¹] [Surface Tension] = [M¹ L⁽¹⁻¹⁾ T⁻²] [Surface Tension] = [M¹ L⁰ T⁻²]

The Final Result and SI Unit

Dimensional Formula: [M¹ L⁰ T⁻²]
Because the length dimension cancels out entirely (L⁰), surface tension is independent of length in its final dimensional structure.
SI Unit: Newton per metre (N/m).

Questions and Answers

Does surface tension have the same dimensions as spring constant?+

Yes! The spring constant (k = Force / Extension) is also Force divided by Length. Therefore, the spring constant and surface tension have the exact same dimensional formula: **[M¹ L⁰ T⁻²]**.

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