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

Significant Figures Explained | NEET Physics Notes, Rules, Tricks & Numericals

 - Dr.Sanjaykumar Pawar  

Rectangular Sheet Area and Volume Calculation | Significant Figures NEET Guide

Significant Figures NEET Notes: Learn measurement rules, area-volume formulas, unit conversion, and numerical solving tricks with easy memory techniques.

Internal Links 

Units and Measurements for NEET

Complete Units and Measurements Notes for NEET

Dimensional Analysis

 Learn Dimensional Formula and Applications

Errors in Measurement

Physics Errors and Error Calculation Methods

Scientific Notation

Scientific Notation Rules and Examples

NEET Physics Formula Revision

 Complete NEET Physics Formula Sheet

Numerical Problem Solving Strategy

 How to Solve Physics Numericals Faster

SI Units and Conversion

 SI Units List and Unit Conversion Tricks

NEET Concept Notes: Significant Figures, Area and Volume Calculation

Question

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m and 2.01 cm respectively. Give the area and volume of the sheet to correct significant figures.

Solution (Step by Step)

Given Data:

Quantity	Value	Significant Figures
Length	4.234 m	4
Breadth	1.005 m	4
Thickness	2.01 cm = 0.0201 m	3

Step 1: Convert Unit

Thickness = 2.01 cm

1 cm = 10^-2 m

Thickness = 2.01 × 10^-2 m = 0.0201 m

Step 2: Calculate Area

Area = Length × Breadth

A = 4.234 × 1.005

A = 4.25517 m²

Least significant figures = 4

Area = 4.255 m²

Step 3: Calculate Volume

Volume = Length × Breadth × Thickness

V = 4.234 × 1.005 × 0.0201

V = 0.085527917 m³

Least significant figures = 3

Volume = 0.0855 m³

Short Notes: Significant Figures

• Significant figures show the accuracy of a measurement.
• Final answer should contain the same number of significant figures as the value having the least significant figures.
• All non-zero digits are always significant.
• Zeros between non-zero digits are significant.
• Starting zeros are not significant.

Number	Significant Figures
4.234	4
1.005	4
0.0201	3

Formula Notes

Rectangle Area:
A = l × b

Rectangle Volume:
V = l × b × t

Remember:

• Area uses two dimensions.
• Volume uses three dimensions.
• Always convert units before calculation.

Mnemonics (Easy Memory Tricks)

1. Significant Figures Rule

"Non-zero digits are HERO"

HERO:

• H - Hidden zeros (between numbers) are significant
• E - Ending zeros after decimal can be significant
• R - Real non-zero digits are always significant
• O - Opening zeros are not significant

2. Zero Rule

"शुरू के Zero सोते हैं, बीच के Zero काम करते हैं।"

3. Calculation Method

D-U-F-C-A Method

Letter	Meaning
D	Data पहचानो
U	Unit सही करो
F	Formula लगाओ
C	Calculate करो
A	Accuracy (Significant Figures) check करो

NEET Exam Trick

"पहले Unit, फिर Formula, फिर Calculation, अंत में Significant Figure"

इस तरीके से विद्यार्थी numerical questions को जल्दी और सही तरीके से solve कर सकता है।