Solved Examples on Dimensional Formula
Example 1: Using Dimensional Formula, X= MaLbTc, find the values of a, b, and c for density.
Solution:
To find: Values for a, b, and c
Given:
Quantity = Density
Using the Dimensional Formula,
X = MaLbTc
We know,
Density = (mass/length3)
= M/L3
= M1L-3T0
Comparing with Dimensional Formula, we get,
a = 1, b = -3, c = 0
Answer: a = 1, b = -3, c = 0
Example 2: Determine the Dimensional Formula of velocity.
Solution:
To find: Dimensional formula of velocity
We know,
Velocity = (distance/time)
= [M0L1T-1]
Answer: Dimensional formula for velocity = [M0L1T-1]
Example 3: State and verify the formula for pressure using the Dimensional Formula analysis.
Solution:
The formula for Pressure is given as, P = Force/Area= F/A
Using Dimensional Formula analysis,
Pressure = Force/Area Dimesional formula for LHS = [M1L-1T–2] Dimesional formula for RHS = [M1L1T–2]/[L2] = [M1L-1T–2] Since LHS matches RHS, the given formula for Pressure is verified dimensionally.
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