Dimensional Formula

1. What Is Meant By Dimensional Formula?

The Dimensional Formula of any quantity serves as an expression that shows the powers by which fundamental units must be raised to yield a single unit of that derived quantity. These Dimensional Formula play an important role in establishing relationships between variables in nearly every dimensional equation.

2. How do you Find the Dimensional Formula?

The Dimensional Formula of any quantity can be given by expressing the formula for it and breaking it down in terms of the base dimensions. Using these base dimensions, we can evaluate the dimensional formula for any given quantity.

3. Write down the Dimensional Formula of Frequency.

The Dimensional Formula for frequency is [MT^–2]. Hertz is the unit of frequency. 

4. What Are the Uses of Dimensional Formula?

• To verify whether a formula is dimensionally correct or not.
• Conversion of units from one system to another for any given quantity.
• To establish derivation between physical quantities based on mutual relationships.
• Dimensional Formulae express every physical quantity in terms of fundamental units.

5. Write down the difference between Dimensional Quantities and Dimensional Formula?

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.

6. What is Dimension in mathematics?

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. As per the definition of Dimension, it represents the extent of a point or a line in a specific direction.

7. What are the Important Dimensional Formula?

Length = L Mass = M Time are the important Dimensional Formula.

8. Write down the Limitation of Dimensional Formula.

• It’s important to note that quantities like trigonometric functions, plane angles, and solid angles do not possess defined dimensional formulae since they are inherently dimensionless in nature.
• The applicability of Dimensional Formulas is confined to a specific set of physical quantities.
• They are unable to determine proportionality constants, which can be a drawback in certain situations.
• Dimensional formulas are primarily suitable for addition and subtraction operations, limiting their use in other mathematical operations.

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.