Dimensional Formula of Surface Tension Explained for JEE Mains
The Dimensional formula of surface tension is really important in physics because it shows how surface tension is connected to things like mass, length and time. For people who want to take the JEE Mains it is very important to understand this formula, which is usually written as [M1 L0 T-2] so they can solve problems about dimensions and fluids correctly. Surface tension is a concept here and understanding its formula will help JEE Mains aspirants, with surface tension problems.
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Understanding Surface Tension Measurement and its Dimensions
To understand surface tension we need to look at what it is. Surface tension is the force that acts on the surface of a liquid. When you draw a line on the surface of a liquid the force acts along that line.
The surface of a liquid acts like a skin because of surface tension. This is much, like a stretched rubber band. Surface tension is what makes the surface of a liquid behave this way.
Surface Tension Unit and Dimension
When we talk about the surface tension unit and dimension we are talking about the measurement of surface tension and the way it is represented mathematically. We are looking at how surface tension's measured and how the surface tension unit is used in math. The surface tension unit is a thing to understand when we are dealing with surface tension and its dimension.
Formula for Surface Tension: The standard mathematical expression is Surface Tension (T or S) = Force (F) / Length (L).
The Surface Tension Unit is really important. Surface Tension Unit is measured in ways. In the SI system people use Newton per meter to measure Surface Tension Unit. This is often written as N/m. On the hand the CGS system is different. In the CGS system Surface Tension Unit is measured in Dynes, per centimeter. This is often written as dyn/cm.
The dimensional formula of surface tension is derived directly from this relationship. Since Force has the dimensions [M L T-2] and Length has the dimension [L], dividing the two results in the length dimensions cancelling out, leaving us with [M T-2].
Deriving the Dimensional Formula of Surface Tension
For students who are getting ready for exams it is really important to understand how to figure out the formula for surface tension. We can look at what the experts, at Vedantu and Allen have to say and break it down into steps.
Identify the Base Formula: Surface Tension = Force / Length
The Break Down Force is something we should understand. Force is basically the product of Mass and Acceleration. To break it down the dimensional formula of the Break Down Force is Mass multiplied by Acceleration, which's [M] times [L T-2]. This equals [M L T-2]. The Break Down Force is a concept that involves the Break Down Force formula.
Apply the Division: Dimensional Formula of Surface Tension = [M L T-2] / [L]
Final Result: When we simplify the expression, the Length in the numerator and the Length in the denominator cancel each other out. This is because Length to the power of 1 divided by Length to the power of 1 equals Length to the power of 0. So the dimensions of the expression are Mass to the power of 1 Length to the power of 0 and Time, to the power of -2 which can be written as [M1 L0 T-2].
So surface tension is really, about the mass and the time. It does not matter how long the surface is where it is happening. Surface tension is still the same it just depends on the mass and the time. Surface tension is not affected by the length of the surface.
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Practical Implications in JEE Mains
In the context of JEE Mains, the dimensional formula of surface tension is often used in "Principle of Homogeneity" questions. For instance, if an equation involves surface tension, surface energy, and area, students must verify that the dimensions on both sides of the equation match. Interestingly, surface tension and surface energy per unit area share the same dimensions, a fact often tested in multiple-choice questions.
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Frequently Asked Questions (FAQs)
1. What is the SI unit and dimensional formula of surface tension?
Ans. The SI unit of surface tension is Newton per meter (N/m). The dimensional formula of surface tension is [M1 L0 T-2], signifying it depends on mass and the square of time (inversely) but not on length.
2. Is the surface tension unit the same in all systems?
Ans. No the unit for this is different. The SI unit is Newtons per meter. The CGS unit is Dynes, per centimeter. But surface tension is always measured with the dimensions, which are Mass Time squared, no matter what system of units we use the surface tension dimensions are always Mass Time squared.
3. How is the formula for surface tension used to find its dimensions?
Ans. You can plug in the values for Force [M L T-2] and Length [L] into the formula T = F/L. When you divide them, the L part goes away, which gives you the final dimensional expression.
4. Why is surface tension independent of length in its dimensional formula?
Ans. The formula for surface tension has length (F/L) in it, however the length in the numerator (from Force) and the length in the denominator (Length itself) cancel each other out. This means that surface tension is a "per unit length" measurement, which makes the ultimate dimension L to the power of 0.
5. Where can I find the best IIT JEE Books for practicing dimensional analysis?
Ans. The PW Storehas a lot of highly recommended IIT JEE Books that go into great detail about surface tension and other physics topics. These books have solved problems and questions from prior years to help you learn the dimensional formula for surface tension.
