Dimensional Formula and Dimensional Equations
The equations resulting from equating a physical quantity to its dimensional formula are termed Dimensional Equations. These equations are an important tool for representing physical quantities in terms of fundamental units. Dimensional formulas for specific quantities used as a foundation for establishing relationships between those quantities within any given dimensional equation.
For example, consider a physical quantity denoted as Y, which depends on the fundamental quantities M (mass), L (length), and T (time) with respective powers a, b, and c. The dimensional formula for this physical quantity [Y] can be expressed as:
[Y] = [MaLbTc]
As examples:
- The dimensional equation for velocity ‘v’ is expressed as [v] = [M0L1T-1].
- The dimensional equation for acceleration ‘a’ is denoted as [a] = [M0L1T-2].
- The dimensional equation for force ‘F’ is given as [F] = [M1L1T-2].
- The dimensional equation for energy ‘E’ is represented as [E] = [M1L2T-2].
- These dimensional equations provide a way to understand and represent various physical quantities in terms of their fundamental units.
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Dimensional Formula
Dimensional Formulas play an important role in converting units from one system to another and find numerous practical applications in real-life situations. Dimensional Formulas are a fundamental component of the field of units and measurements. In mathematics, Dimension refers to the measurement of an object’s size, extent, or distance in a specific direction, such as length, width, or height, but in the context of physical quantities, the dimension signifies the exponent to which fundamental units must be raised to yield a single unit of that specific quantity.
In this article, we will discuss the introduction, definition, properties, and limitations of a Dimensional Formula and its meaning. We will also understand dimensional formulas for different physical quantities and Dimensional equations. We will also solve various examples and provide practice questions for a better understanding of the concept of this article. We have to study Dimensional Formula in Class 11.
Table of Content
- What is Dimensional Formula?
- Dimensional Formula for Various Quantities
- Application of Dimensional Formula
- Limitations of Dimensional Formula
- Dimensional Formula and Dimensional Equations