NEET Physics Dimensional Analysis Notes | Relativistic Mass Formula with Easy Tricks

 - Dr.Sanjaykumar Pawar  

Dimensional Analysis Class 11 Notes | NEET Smart Notes with MCQs & Mnemonics 

NEET Smart Notes: Learn Dimensional Analysis and the Relativistic Mass Formula with easy tricks, mnemonics, and quick revision.

NEET Smart Notes

Topic: Dimensional Analysis (Relativistic Mass Formula)

Part 1 : Questions & Answers

Q1. A famous relation in physics relates moving mass (m) to the rest mass (m₀) of a particle in terms of its speed (v) and the speed of light (c). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes:

m / m₀ = (1 − v²)^−1/2

Guess where to put the missing constant c.

Step 1:
The left side is

m / m₀

Both m and m₀ are masses. Therefore,

m / m₀ → Dimensionless

---

Step 2:
The quantity inside the bracket must also be dimensionless. The number 1 has no unit. But

v²

has dimensions

L²T⁻²

Therefore,

1 − v²

is dimensionally incorrect.

---

Step 3: Speed of light (c) has the same dimensions as speed (v).

[c] = LT⁻¹

Therefore,

v² / c²

becomes dimensionless.

---

Correct Formula

m / m₀ = (1 − v² / c²)^−1/2

or

m = m₀ / √(1 − v²/c²)

Part 2 : Short Notes

Definition
Dimensional analysis is a method used to check whether a physical equation is correct by comparing the dimensions of both sides.

Important Rule
Only quantities having the same dimensions can be added or subtracted.

Dimension of Speed
Speed (v) = LT⁻¹

Dimension of Speed of Light
c = LT⁻¹

Dimension of v²
L²T⁻²

Dimension of c²
L²T⁻²

Dimensionless Quantity
v²/c² has no dimensions.

Golden Rule
Whenever "1" appears in a formula, the quantity added or subtracted with it must also be dimensionless.

Correct Formula

m / m₀ = (1 − v²/c²)^−1/2

Part 3 : Memory Mnemonics

Mnemonic 1

• Same Unit → Same Suit
• Addition and subtraction are possible only between quantities having the same dimensions.

Mnemonic 2

• Speed Meets Speed
• v must always be compared with another speed, i.e., c.
• Remember: v/c is dimensionless.

Mnemonic 3

• One Loves Zero Dimension
• If "1" appears inside a bracket, the other quantity must also be dimensionless.

Mnemonic 4

• Square with Square
• Whenever v² appears, divide it by c².

Final Memory Formula

m / m₀ = (1 − v²/c²)^−1/2

 Internal Links

Class 11 Physics Units and Measurements Notes

SI Units and Fundamental Quantities

Errors in Measurement Notes

Significant Figures Explained

Dimensional Formula Shortcut Tricks

Method of Dimensions for Derivations

Vector and Scalar Quantities Notes

Motion in One Dimension Notes

Motion in Two Dimensions Notes

Laws of Motion Complete Notes

Work, Energy and Power Notes

Gravitation Formula Sheet

Oscillations and SHM Notes

Waves Complete Revision Notes

NCERT Physics Important Formula Book

NEET Physics Chapter-wise MCQs

Previous Year NEET Physics Questions

Physics One-Page Revision Sheets

NEET Physics Mind Maps

NEET Physics Formula Handbook