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.
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.
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
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]
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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