107 LearnersLast updated on August 5th, 2025
Dimensional Formula
In physics, dimensional formulas provide a way to express the dimensions of a physical quantity in terms of base quantities like mass, length, and time. A dimensional formula is used to represent the nature of the physical quantity. In this topic, we will learn about the dimensional formula and its significance.
List of Dimensional Formulas
Dimensional analysis is an essential tool in physics and engineering to understand the relationship between different physical quantities. Let’s learn how to express physical quantities using dimensional formulas.
Dimensional Formula for Velocity
Velocity is the rate of change of displacement with respect to time.
The dimensional formula for velocity is given by: [ [M0L1T{-1}] ] where M is mass, L is length, and T is time.
Dimensional Formula for Force
Force is the interaction that changes the motion of an object.
The dimensional formula for force is: [ [M1L1T{-2}] ] This is derived from Newton's second law, ( F = ma ), where m is mass and a is acceleration.
Dimensional Formula for Energy
Energy is the capacity to do work.
The dimensional formula for energy is: [ [M1L2T{-2}] ] This can be derived from the work-energy principle: work done = force × distance.
Importance of Dimensional Formulas
Dimensional formulas help in checking the correctness of physical equations, converting units, and understanding the relationship between different physical quantities.
Here are some important points about dimensional formulas:
- They provide a method for checking the consistency of equations.
- By learning dimensional formulas, students can understand concepts like unit conversion and dimensional analysis.
- Dimensional formulas help in deriving relations between physical quantities.
Tips and Tricks to Memorize Dimensional Formulas
Students often find dimensional formulas tricky and confusing.
Here are some tips to master them:
- Use mnemonics to remember base dimensions like M for mass, L for length, and T for time.
- Relate the dimensional formulas with real-life scenarios, such as imagining physical quantities in terms of their dimensional units.
- Use flashcards to memorize the formulas and rewrite them for quick recall. Create a chart for a quick reference.
Common Mistakes and How to Avoid Them While Using Dimensional Formulas
Students make errors when working with dimensional formulas. Here are some mistakes and ways to avoid them:
Mistake 1
Confusing base quantities
Students sometimes confuse the base quantities like mass, length, and time.
To avoid confusion, always remember the fundamental base quantities and their symbols: M for mass, L for length, and T for time.
Mistake 2
Misapplying dimensions in derived formulas
When deriving dimensional formulas, students may apply dimensions incorrectly.
Always check that each term in an equation has the same dimension to ensure correctness.
Mistake 3
Neglecting dimensionless quantities
Students assume that every term has dimensions, but some quantities are dimensionless, like angles in radians.
Identify and acknowledge dimensionless quantities in calculations.
Mistake 4
Ignoring unit conversion
Students often overlook the need to convert units when using dimensional formulas.
Always ensure that units are consistent and correctly converted when necessary.
Mistake 5
Overlooking the power of dimensions
When calculating or deriving formulas, students sometimes miss the powers of dimensions.
Ensure that each dimension is raised to the correct power in the formula.
Examples of Problems Using Dimensional Formulas
Problem 1
What is the dimensional formula for acceleration?
The dimensional formula for acceleration is [ [M0L1T{-2}] ].
Explanation
Acceleration is the rate of change of velocity with respect to time.
The dimensional formula for velocity is [ [M0L1T{-1}] ].
Therefore, acceleration, which is velocity per unit time, has the dimensional formula [ [M0L1T{-2}] ].
Problem 2
Find the dimensional formula of pressure.
The dimensional formula for pressure is [ [M1L1T{-2}] ].
Explanation
Pressure is defined as force per unit area.
Since force has the formula [ [M1L1T{-2}] ] and area has the formula [ [L2] ], the dimensional formula for pressure is [ [M1L1T{-2}] ]
Problem 3
Determine the dimensional formula for momentum.
The dimensional formula for momentum is [ [M1L1T{-1}] ]
Explanation
Momentum is defined as the product of mass and velocity.
The dimensional formula for mass is \[ [M^1] \] and for velocity is [ [M0L1T{-1}] ].
Thus, the dimensional formula for momentum is [ [M1L1T{-1}] ].
Problem 4
What is the dimensional formula for power?
The dimensional formula for power is [ [M1L2T{-3}] ].
Explanation
Power is defined as the rate of doing work.
Since work has the dimensional formula [ [M1L2T{-2}] ] and power is work per unit time, the dimensional formula for power is [ [M1L2T{-3}] ].
Problem 5
Find the dimensional formula for frequency.
The dimensional formula for frequency is \[ [M^0L^0T^{-1}] \].
Explanation
Frequency is defined as the number of cycles per unit time.
As it is the reciprocal of time period, the dimensional formula for frequency is [ [M0L0T{-1}] ]
FAQs on Dimensional Formulas
1.What is a dimensional formula?
2.How is the dimensional formula for energy derived?
3.Why is dimensional analysis important?
4.Can dimensional formulas determine the units of a quantity?
5.What are dimensionless quantities?
Glossary for Dimensional Formulas
- Dimensional Formula: An expression showing how a physical quantity is related to base quantities like mass, length, and time.
- Base Quantities: Fundamental physical quantities (mass, length, time) used to derive other quantities.
- Dimensional Analysis: A technique to check the consistency of equations and convert units by analyzing dimensions.
- Dimensionless Quantity: A quantity without any physical dimension, often a pure number or a ratio.
- Derived Quantities: Physical quantities derived from base quantities, such as velocity or force.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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