How to Derive the Dimensional Formula for Surface Tension in Physics?
The Dimensions Of Surface Tension tell us how this property, seen in water droplets or soap bubbles, fits into fundamental physics. For JEE Main, connecting physical effects like this to their formulas and dimensional analysis is essential. Knowing the dimensional formula streamlines quick calculations and error-checking in physics problems.
Surface tension explains why liquid surfaces behave like stretched membranes. This is crucial when solving fluid mechanics questions or understanding phenomena like capillary action. A clear grip over the dimensional formula of surface tension makes it easier to answer conceptual as well as numerical problems. For related practice, see surface tension and contact angle or capillary action for JEE Main-level contexts.
Many JEE aspirants confuse units and dimensions. While the SI unit of surface tension and its expression in MLT notation look different, both sharpen your approach to dimensional analysis and exam performance.
Dimensions Of Surface Tension: Formula, Unit, and Quick Facts
The primary formula for surface tension (T) is basic yet powerful:
- Surface tension = Force ( F ) per unit length ( L )
- Mathematically, T = F / L
- SI unit: newton per metre (N/m)
- Dimensional formula: [M1L0T-2]
- Example: For water at 20°C, T ≈ 0.072 N/m
| Quantity | Symbol | SI Unit | Dimensional Formula |
|---|---|---|---|
| Surface Tension | T | N/m | [M1L0T-2] |
| Force | F | N | [M1L1T-2] |
| Length | L | m | [M0L1T0] |
Step-by-Step Derivation: Dimensions Of Surface Tension
Let’s derive the surface tension dimensional formula in M, L, T format as asked in JEE Main:
- Start with the definition: Surface tension T = Force / Length
- Force (F) has dimensions [M1L1T-2]
- Length (L) has dimensions [M0L1T0]
- So, T = [M1L1T-2] / [M0L1T0]
- Dividing, we get [M1L0T-2]
Thus, Dimensions Of Surface Tension = [M1L0T-2] (boxed in your answer). Mastering this step ensures you select or check formulae accurately in the exam.
Applications, Numericals & Pitfalls with Dimensions Of Surface Tension
Understanding surface tension dimensions in MLT assists in unit conversions, verifying relationships, and solving competitive exam numericals.
- To check if a formula is dimensionally correct, compare both sides using [M, L, T] exponents.
- Example question: “Is energy per unit area the same as surface tension?”
- Energy per area [ML0T-2] matches surface tension, so formulas are equivalent.
- Easy mistake: Mixing up dimensions of stress ([ML-1T-2]) and surface tension—stress involves area, not length.
- Always double-check numerators and denominators when handling force, energy, or work problems.
Practice is vital. Try dimensional analysis tricks in problems from units and dimensions or dimensional analysis and its applications. For full-length exercises, check JEE question sets on properties of solids and liquids or actual mock test series.
| Problem | Solution Steps | Result |
|---|---|---|
| Check if T = Energy / Area |
|
Dimensionally correct |
| Compare with stress ([ML-1T-2]) |
|
Different from surface tension |
Related Quantities and Comparing Dimensions: Surface Tension, Energy, Stress
Understanding links between dimensions of surface energy, stress, tension, and related forces is a high-yield JEE skill. Use dimensional formulas to compare these easily in competitive exams.
- Surface energy is another way to express surface tension. Both have [M1L0T-2].
- Stress and pressure involve force per area, giving [M1L-1T-2]—distinct from surface tension.
- Force per unit length arises in both surface tension and line tension questions.
- Spotted a formula error? Dimensional mismatch highlights the problem instantly.
For further insight, see dimensions of work, force, and stress for rapid cross-referencing.
| Physical Quantity | Expression | Dimensions |
|---|---|---|
| Surface Tension | Force per unit length | [M1L0T-2] |
| Surface Energy | Work per unit area | [M1L0T-2] |
| Stress | Force per unit area | [M1L-1T-2] |
| Pressure | Force per unit area | [M1L-1T-2] |
Dimensional formulas support error-checking, quick revision, and robust JEE preparation. For systematic study, visit units and dimensions and related dimensional analysis resources on Vedantu.
Summary Table: Dimensions Of Surface Tension
| Key Feature | Value/Formula |
|---|---|
| Formula | T = F / L |
| SI Unit | N/m |
| Dimensional Formula | [M1L0T-2] |
| Physical Meaning | Force required per unit length on the surface |
| Key Competency Area | Dimensional analysis, fluid mechanics, surface energy |
Remember, Dimensions Of Surface Tension simplify formula validation, error detection, and ensure efficient revision in JEE Main. Mastering these basics boosts your confidence in both theory and numericals.
For even deeper practice on dimensional analysis or related surface physics, explore additional topic notes or exercises available on Vedantu’s JEE Main Physics section.
FAQs on Dimensions of Surface Tension Explained for JEE, NEET & Boards
1. What is the dimensional formula for surface tension?
Surface tension has the dimensional formula [M1L0T-2]. This is because surface tension is defined as force per unit length.
Key points:
- Force has dimensions: [M1L1T-2]
- Length has dimensions: [L1]
- Therefore, surface tension = force/length = [M1L1T-2] / [L1] = [M1L0T-2]
2. What is the dimension of surface tension in MLT?
The dimension of surface tension in MLT notation is [M1L0T-2].
Explanation:
- Mass (M): 1
- Length (L): 0
- Time (T): -2
3. What is the SI unit of surface tension?
The SI unit of surface tension is newton per meter (N/m).
Additional points:
- N/m is used in Physics problems and is recognized internationally.
- Sometimes, surface tension is also expressed in dyne/cm in the CGS system.
4. How is surface tension related to force and length?
Surface tension is mathematically defined as the force per unit length acting on a liquid surface.
- Surface tension = Force / Length
- Formula: T = F/l, where T is surface tension, F is the tangential force, and l is length.
- This relationship explains why surface tension has the dimensions [M1L0T-2].
5. Is the unit of surface tension N/m?
Yes, the SI unit of surface tension is newton per meter (N/m).
This unit shows that surface tension represents the force (in newtons) acting along a line of one meter length on a liquid surface. It is widely used in experiments and numericals involving liquid interfaces.
6. Can surface tension have units of pressure? Why or why not?
Surface tension and pressure have similar dimensions but represent different concepts.
- Pressure = Force/Area, while Surface tension = Force/Length.
- Surface tension (N/m) and pressure (N/m2) have different physical meanings, even though their dimensional formulas are related.
- Surface tension acts along a line, not over an area.
7. Do all liquids have the same dimensional formula for surface tension?
Yes, the dimensional formula for surface tension is the same for all liquids: [M1L0T-2].
However:
- The numerical value of surface tension varies from one liquid to another (e.g., water, mercury, oil).
- Only the dimensional formula remains constant as it reflects the nature of the physical quantity, not its magnitude.
8. How can the dimensional formula of surface tension help in dimensional analysis?
The dimensional formula of surface tension helps check the correctness of formulas involving this quantity.
- By confirming that both sides of an equation have consistent dimensions (for example, in T = F/l), you avoid common mistakes.
- It also assists in unit conversions and identifying errors in derivations or numericals.
9. Is surface tension a scalar or vector quantity?
Surface tension is a scalar quantity.
- It has only magnitude and no direction.
- Although the force due to surface tension acts along the surface, the value (numerical measure) of surface tension itself is scalar.
10. What is the general formula for surface tension in physics?
The general formula for surface tension (T) in physics is:
T = F/l
- Where T = surface tension
- F = force acting on the liquid surface
- l = length over which the force acts
11. What is the difference between dimensions of surface tension and surface energy?
Surface tension and surface energy are related but have different dimensions and meanings.
- Surface tension (T): Dimensions [M1L0T-2], unit N/m (force per unit length)
- Surface energy per unit area: Dimensions [M1L0T-2], unit J/m2 (energy per unit area)
12. How to derive the dimensional formula for surface tension step-by-step?
To derive the dimensional formula for surface tension, follow these steps:
- Start with the formula: T = F/l
- Force (F) has dimensions: [M1L1T-2]
- Length (l) has dimensions: [L1]
- Divide: [M1L1T-2] / [L1] = [M1L0T-2]
