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

Physics Constants Made Easy: Mnemonics, Tricks, Mind Maps & Memory Hacks

  Learn Physics Constants Fast with Mnemonics and Visual Memory Techniques

- Dr.Sanjaykumar Pawar 

🚀 Ultra-Memory Guide for Physics Constants

Instead of memorizing 20+ random numbers, group them into families, patterns, stories, and visual maps.

---

1. MASTER MEMORY TABLE

Constant	Value	Memory Trick
Electron Mass	9.11 × 10⁻³¹ kg	Electron = smallest → 9-11 emergency tiny particle
Proton Mass	1.67 × 10⁻²⁷ kg	Proton ≈ 1836 times heavier than electron
Neutron Mass	1.675 × 10⁻²⁷ kg	Neutron ≈ Proton
Electron Charge	1.6 × 10⁻¹⁹ C	Most important physics number
Speed of Light	3 × 10⁸ m/s	"3 followed by 8 zeros"
Planck Constant	6.626 × 10⁻³⁴	Triple 6 pattern
Gravitation Constant G	6.67 × 10⁻¹¹	G = 667
Avogadro Number	6.022 × 10²³	Mole's phone number
Boltzmann Constant	1.38 × 10⁻²³	Remember 138
Stefan Constant	5.67 × 10⁻⁸	Similar to Wien family
Wien Constant	2.898 × 10⁻³	Near 2.9
Solar Constant	1.366 × 10³	Sun sends 1366 W/m²
Sun Mass	1.989 × 10³⁰	Almost 2 × 10³⁰
Earth Mass	5.97 × 10²⁴	Almost 6 × 10²⁴
Earth Radius	6.4 × 10⁶ m	Easy approximation
Earth Density	5.5 × 10³ kg/m³	5.5
Earth Angular Velocity	7.29 × 10⁻⁵	Daily rotation
Earth-Moon Distance	3.84 × 10⁸ m	Nearly light-second
Earth Magnetic Moment	8.22 × 10²²	822
AU	1.496 × 10¹¹ m	Sun-Earth distance

---

 

Physics Constants Memory Map with Mnemonics, Tables and Visual Learning Techniques for Fast Exam Revision.

2. NUMBER FAMILY TRICK

Most physics constants belong to only a few number families:

Family A: 1.6

Think:

⚡ Charge of Electron

⚡ 1 eV

Both use:

1.6 × 10⁻¹⁹

Electron Charge
      ↓
    1.6
      ↓
    1 eV

---

Family B: 6.6

Think:

📌 Planck Constant

📌 Gravitational Constant

Planck → 6.626
Gravity → 6.67

Both start with 6.6

---

Family C: 6.0

Think:

🧪 Avogadro Number

6.022 × 10²³

Scientists love 6!

---

3. SUBATOMIC PARTICLE STORY

Imagine a family:

👶 Electron (tiny baby)

👨 Proton (big father)

👨‍🦳 Neutron (father's twin brother)

Electron = 9.11 ×10⁻³¹

Proton = 1.67 ×10⁻²⁷

Neutron = 1.675 ×10⁻²⁷

Memory:

"Proton and Neutron are twins."

Only remember one number:

1.67 × 10⁻²⁷

---

4. EARTH FAMILY TRICK

Everything about Earth revolves around 6.

Quantity	Value
Earth Mass	6 ×10²⁴
Earth Radius	6.4×10⁶
Density	5.5×10³

Mnemonic:

🌍 "Earth lives in House Number 6."

---

5. SUN FAMILY TRICK

Think:

☀ Sun is HUGE

Mass = 2 ×10³⁰ kg

Distance to Earth:

AU = 1.5 ×10¹¹ m

Mnemonic:

Sun weighs 2 and lives 1.5 away.

---

6. SPACE DISTANCE MEMORY CHAIN

Moon → Earth
3.84×10⁸ m

Sun → Earth
1.5×10¹¹ m

Light Year
9.46×10¹⁵ m

Visual ladder:

Moon
  ↓
10⁸

Sun
  ↓
10¹¹

Light Year
  ↓
10¹⁵

Every step jumps by about 10³–10⁴.

---

7. CONVERSION TRICKS

Conversion	Memory
1 Å	10⁻¹⁰ m
1 Fermi	10⁻¹⁵ m
1 eV	1.6×10⁻¹⁹ J
1 AU	1.5×10¹¹ m
1 Light Year	9.46×10¹⁵ m
1 HP	746 W

Tiny Length Ladder

Angstrom
10⁻¹⁰

↓ smaller

Fermi
10⁻¹⁵

Difference = 10⁵

---

8. SI BASE UNITS MEMORY SENTENCE

The 7 SI base units:

Quantity	Unit
Length	metre
Mass	kilogram
Time	second
Temperature	kelvin
Current	ampere
Amount	mole
Luminous Intensity	candela

Mnemonic:

"My King Takes Tea And Makes Cool Coffee"

My       → Metre
King     → Kilogram
Takes    → Time (second)
Tea      → Temperature
And      → Ampere
Makes    → Mole
Cool     → Candela
Coffee

---

9. QUICK EXAM CRAM SHEET

Must-Know Constants

c = 3×10⁸

e = 1.6×10⁻¹⁹

h = 6.626×10⁻³⁴

G = 6.67×10⁻¹¹

NA = 6.022×10²³

kB = 1.38×10⁻²³

Remember:

3, 1.6, 6.6, 6.0, 1.38

These five numbers solve most physics MCQs.

---

🧠 Mind Map

                    PHYSICS CONSTANTS
                           │
      ┌────────────────────┼────────────────────┐
      │                    │                    │
  Atomic               Universal             Earth
      │                    │                    │
 Electron             c=3×10⁸          Radius=6.4×10⁶
 Proton               h=6.626          Mass=6×10²⁴
 Neutron              G=6.67           Density=5.5×10³
 Charge=1.6           NA=6.022
                       kB=1.38
      │                    │
      └|────────────┬───────|Astronomy
    Constant                        │
     Plunk constant             AU=1.5×10¹¹
Gravitation constant            Moon=3.84×10⁸
Boltzmann Constant              Sun=2×10³⁰
Stefan Constant
Wien Constant
Solar Constant                  LY=9.46×10¹⁵
               
   

🎯 30-Second Revision Formula

Remember only:

3, 1.6, 6.6, 6.0, 1.38, Earth=6, Sun=2, AU=1.5

From these anchor numbers, most of the listed constants can be reconstructed during exams. 

INTERNAL LINKS

SI Units and Dimensional Analysis Explained

Complete Physics Formula Handbook

Motion and Kinematics Quick Revision Notes

Work, Energy and Power Formula Sheet

Electromagnetism Mind Maps and Memory Tricks

Modern Physics Notes for Competitive Exams

Thermodynamics Formula Cheat Sheet

Waves and Optics Revision Guide

Astronomy and Space Physics Basics

JEE Physics One-Page Revision Notes

Physics Constants & Units

A comprehensive memory toolkit designed to lock these physics constants, units, and conversion factors directly into your long-term memory using memory anchors, pattern-recognition tricks, and structural maps.

1. Master Reference Table (The Pattern Identifier)

Before diving into mnemonics, let's fix a subtle typo in your source list and organize these numbers by their powers of 10 to help your brain spot structural patterns.

Note: The speed of light (c) is accurately represented here as 3 × 10⁸ m/s for standard vacuum calculations.

Constant / Unit	Symbol	Value & Unit	The Pattern / Anchor Trick
Mass of Electron	me	9.109 × 10-31 kg	9-10-11 sequence (9.109 × 10-31)
Mass of Proton	mp	1.6726 × 10-27 kg	1.67 is standard; Proton has 2 (1.6726)
Mass of Neutron	mn	1.6749 × 10-27 kg	Neutron is heavier than proton; has 4 (1.6749)
Electron Charge	e	-1.602 × 10-19 C	Sweet 16 (1.6) and coming of age (19)
Speed of Light	c	3 × 108 m/s	Classic absolute constant.
Planck's Constant	h	6.626 × 10-34 J·s	6.6 and 3 halves to 4
Universal Gravitation	G	6.67 × 10-11 N·m²/kg²	6, 7, 11 (Convenience store numbers)
Avogadro's Number	NA	6.022 × 1023 mol-1	22nd of October (6.022 × 1023)
Boltzmann Constant	kB	1.38 × 10-23 J/K	1, 2, 3 sequence hidden: 1.38 × 10-23
Stefan's Constant	σ	5.67 × 10-8 W·m-2·K-4	Sequential count: 5, 6, 7, 8
Wien's Constant	b	2.898 × 10-3 m·K	Almost 3 × 10-3
Solar Constant	S	1.366 × 103 W·m-2	1366 (A year in history style)
Mass of Sun	Ms	1.989 × 1030 kg	Taylor Swift's album 1989
Mass of Earth	ME	5.97 × 1024 kg	Almost 6 × 1024
Radius of Earth	Re	6.4 × 106 m (or 6371 km)	64 Lakh meters
Density of Earth	ρ	5.513 × 103 kg/m³	Roughly 5.5 times water density (103)
Angular Velocity (Earth)	ω	7.29 × 10-5 rad/s	7.3 × 10-5
Astronomical Unit	AU	1.496 × 1011 m	Roughly 1.5 × 1011
Earth-Moon Distance	dem	3.844 × 108 m	38-44 pattern
Earth's Mag. Moment	M	8.22 × 1022 A·m²	Triple 2s and 8s

2. High-Impact Memory Mnemonics & Tricks

The Atomic Trio (Masses & Charge)

• Electron Mass (m_e = 9.1 × 10^-31): Notice the digit run. 9 point 1 × 10^-31. Think: "An electron is so light it fell down a 9 to 1 slide, all the way to -31."
• Proton (1.672 × 10^-27) vs. Neutron (1.674 × 10^-27): Both share 1.67 × 10^-27.
  • To remember which is heavier: Protons have 2 legs (1.672), Neutrons have 4 legs (1.674). A Neutron is always Noticeably heavier than a Proton.
• Electron Charge (-1.6 × 10^-19): Remember "Sweet 16 at 19". The value is 1.6, the power is -19.

The Astrophysics Quantities

• Stefan's Constant (σ = 5.67 × 10^-8): This is the easiest constant in physics because it counts sequentially: 5, 6, 7, 8.
• Universal Gravitational Constant (G = 6.67 × 10^-11): Think of the convenience store chain 7-Eleven. Roll back slightly to 6.67 and couple it with -11.
• Mass of the Sun (1.989 × 10³⁰): The Sun loves music. Its mass starts exactly with the year 1989 (1.989). The power is a round, hot 30.

3. Visual Concept Mapping

The Space Distance Ladder (From Smallest to Largest)

To remember distances and conversion coefficients intuitively, map them step-by-step out into space:

[ Earth ] 
    │
    ├─► Radius of Earth (Re) = 6.4 x 10⁶ m
    │
    ├─► Earth-Moon Distance = 3.84 x 10⁸ m (Same power of 10 as Speed of Light!)
    │
    ├─► 1 A.U. (Earth to Sun) = 1.496 x 10¹¹ m
    │
    └─► 1 Light Year (Interstellar) = 9.46 x 10¹⁵ m
        

Micro-Scale Distance Hierarchy

Use this visualization ladder to never mix up your microscopic conversions:

1 Meter ──► 1 Ångström (10⁻¹⁰ m) ──► 1 Fermi (10⁻¹⁵ m)
              [Atomic Scale]            [Nuclear Scale]
            

• Mnemonic: A comes before F in the alphabet, just like -10 comes before -15 on the number line.

4. SI Base Units Breakdown Chat Matrix

When navigating the fundamental systems of units (CGS, FPS, MKS, MKSA), you only need to look at the letters themselves to know what they measure:

[C]entimeter   [G]ram       [S]econd
[F]oot         [P]ound      [S]econd
[M]eter        [K]ilogram   [S]econd
[M]eter        [K]ilogram   [S]econd    [A]mpere
            

The 7 Fundamental Pillars of SI

Base Dimension	Unit Name	Symbol	Quick Brain Anchor
Length	metre	m	Standard stride
Mass	kilogram	kg	A liter of water
Time	second	s	Heartbeat pace
Temperature	kelvin	K	No degree symbol (°) allowed!
Electric current	ampere	A	Current flow
Amount of substance	mole	mol	Chemistry's dozen
Luminous intensity	candela	cd	Brightness of 1 standard candle

5. Instant Association Flash-Tricks

• 1 Horsepower = 746 Watts: Think of a mythical mechanical horse running down Route 746.
• 1 eV = 1.6 × 10^-19 J: You do not need to memorize this separately! It is exactly identical to the magnitude of the charge of an electron.
• Boltzmann Constant (k_B = 1.38 × 10^-23): Notice the pattern: 1, 2, 3. 1.38 × 10^-23. The digits 1, 2, and 3 are all present in the structural layout!