Units & Dimensions Change of Unit System Explained | NEET Physics Tricks

 - Dr.Sanjaykumar Pawar  

Calorie to Joule Conversion | Dimensional Analysis Shortcut for NEET 

“Change of Unit System in Physics: Calorie to Joule using α β γ dimensional analysis trick”

🔗INTERNAL LINKS

/physics/units-and-dimensions-basics

/physics/dimensional-analysis-tricks

/physics/change-of-unit-system-examples

/physics/energy-units-and-conversion

/neet/physics-important-formulas

/neet/physics-shortcuts-and-mnemonics

/cbse-class-11-physics-chapter-1-notes

/CBSE class 11 physics chapter 1 solution

📘 Units, Dimensions & Change of Unit System

📌 Question (CBSE Style)

1.3 A calorie is a unit of heat (energy in transit) and it equals about 4.2 J where 1 J = 1 kg m² s⁻². Suppose we employ a system of units in which the unit of mass equals α kg, the unit of length equals β m, and the unit of time is γ s. Show that a calorie has a magnitude 4.2 α⁻¹ β⁻² γ² in terms of the new units.

📌 Solution (Step-by-Step)

Step 1: Relation between calorie and Joule

1 calorie = 4.2 J

Step 2: SI unit of Joule

1 J = 1 kg m² s⁻²

So,

1 calorie = 4.2 kg m² s⁻²

Step 3: New unit system

Mass unit = α kg
Length unit = β m
Time unit = γ s

Therefore:

1 kg = α⁻¹
1 m = β⁻¹
1 s = γ⁻¹

Step 4: Substitute into energy expression

1 J = (α⁻¹)(β⁻¹)²(γ⁻¹)⁻²

Simplifying:

1 J = α⁻¹ β⁻² γ²

Step 5: Multiply by 4.2

1 calorie = 4.2 α⁻¹ β⁻² γ²

📌 Final Answer

1 calorie = 4.2 α⁻¹ β⁻² γ² (in new system of units)

📘 Complete Notes

🔷 1. Concept of Unit System Change

When the unit system changes, physical quantities remain same but their numerical values change.

🔷 2. Dimensional Formula of Energy

Energy = [M L² T⁻²]

🔷 3. General Rule

If Q = [Mᵃ Lᵇ Tᶜ]

New value = Old value × α⁻ᵃ β⁻ᵇ γ⁻ᶜ

🔷 4. Key Example

1 calorie = 4.2 α⁻¹ β⁻² γ²

🔷 5. Important Points

• SI units are always the starting point.
• Always convert base units first.
• Use dimensional formula for quick solving.
• Negative exponents appear due to reciprocal conversion.

🔷 6. Exam Tips

• Write dimensional formula first.
• Apply power rule carefully.
• Check signs of exponents.
• Keep final answer boxed.

📘 NEET PRACTICE QUESTIONS – UNITS, DIMENSIONS & CHANGE OF UNIT SYSTEM

🟢 TYPE 1: Direct MCQs (Single Correct Option)

Easy

Q1. 1 calorie is equal to:

A) 4.2 N
B) 4.2 J
C) 42 J
D) 0.42 J

Answer: B

Q2. Dimensional formula of energy is:

A) [M L T⁻¹]
B) [M L² T⁻²]
C) [M² L T⁻²]
D) [M L⁻¹ T⁻²]

Answer: B

Moderate

Q3. Energy in new system (α, β, γ units) is:

A) α β² γ⁻²
B) α⁻¹ β⁻² γ²
C) α² β⁻¹ γ⁻²
D) α β⁻² γ²

Answer: B

Q4. Dimensional formula of pressure is:

A) [M L T⁻²]
B) [M L⁻¹ T⁻²]
C) [M L² T⁻²]
D) [M⁻¹ L T⁻²]

Answer: B

Hard

Q5. If M=2, L=3, T=5 then force changes by:

A) 2³/5²
B) 2×3×5⁻²
C) 2×3⁻¹×5²
D) 2×3×5²

Answer: B

🟡 TYPE 2: Statement-Based Questions

Q6.

Statement I: Energy has dimensional formula [M L² T⁻²]

Statement II: Energy depends on mass, length and time

A) Both true and II explains I
B) Both true but II not explanation
C) I true, II false
D) I false, II true

Answer: A

Q7.

Statement I: Numerical value changes when unit changes

Statement II: Physical quantity remains constant

A) Both true and II explains I
B) Both true but no relation
C) I true II false
D) I false II true

Answer: A

🔵 TYPE 3: Assertion & Reason

Q8.

Assertion (A): Energy = [M L² T⁻²]

Reason (R): Energy = Force × distance

A) Both true and R explains A
B) Both true but R not explanation
C) A true R false
D) A false R true

Answer: A

Q9.

Assertion (A): Time exponent becomes positive in conversion

Reason (R): Time unit is inverted (γ⁻¹) in new system

A) Both true and R explains A
B) Both true but no relation
C) A true R false
D) A false R true

Answer: A

🟣 TYPE 4: Match the Columns

Q10. Match Column I with Column II

Column I:
A. Force
B. Energy
C. Pressure
D. Velocity

Column II:
1. [L T⁻¹]
2. [M L T⁻²]
3. [M L² T⁻²]
4. [M L⁻¹ T⁻²]

Answer: A-2, B-3, C-4, D-1

🟠 TYPE 5: Conceptual / Diagram Type

Q11. Which quantity is represented by [M L² T⁻²]?

A) Force
B) Energy
C) Velocity
D) Pressure

Answer: B

Q12. If unit decreases and numerical value increases, then quantity is:

A) Directly proportional to unit
B) Inversely proportional to unit
C) Independent of unit
D) Zero dimension

Answer: B

🔥 NEET QUICK TRICK

✔ Energy = M¹L²T⁻² → α⁻¹ β⁻² γ²
✔ Always flip sign of exponents in new unit system
✔ Use dimensional formula first, solve in 10 seconds

📘 Units & Dimensions - NEET Master Notes

📊 1. Master Table Chart

Physical Quantity	Dimensional Formula	Shortcut Memory
Mass	[M¹ L⁰ T⁰]	Only M
Length	[M⁰ L¹ T⁰]	Only L
Time	[M⁰ L⁰ T¹]	Only T
Velocity	[M⁰ L¹ T⁻¹]	Distance/Time
Acceleration	[M⁰ L¹ T⁻²]	v/t
Force	[M¹ L¹ T⁻²]	F = ma
Energy	[M¹ L² T⁻²]	Force × distance
Power	[M¹ L² T⁻³]	Work/time
Pressure	[M¹ L⁻¹ T⁻²]	Force/area

🧠 2. Mnemonic Tricks

🔥 Force Family Mnemonic: "FAVEP"

• F → Force = M¹L¹T⁻²
• A → Acceleration = L¹T⁻²
• V → Velocity = L¹T⁻¹
• E → Energy = M¹L²T⁻²
• P → Pressure = M¹L⁻¹T⁻²

🔥 Change of Units Trick: "MLT Flip Rule"

If Q = [Mᵃ Lᵇ Tᶜ]

Then: Q(new) = Q(old) × α⁻ᵃ β⁻ᵇ γ⁻ᶜ

⚡ 3. NEET Fast Trick Method

1. Write dimensional formula
2. Note powers of M, L, T
3. Apply sign flip rule
4. Multiply constants if given

🔥 Final Shortcut: Just flip exponents and multiply!

📌 4. Calorie Example (Trick Application)

Given: 1 calorie = 4.2 J

Joule dimension:

1 J = [M¹ L² T⁻²]

Apply unit system:

Mass → α⁻¹
Length → β⁻²
Time → γ²

Final Answer:

1 calorie = 4.2 α⁻¹ β⁻² γ²

🧩 5. Memory Story Trick

Imagine a physics world with 3 rulers:

• Mass ruler = α
• Length ruler = β
• Time ruler = γ

When rulers change, value changes inversely → exponents flip automatically.

🎯 6. One-Line Revision

“M power flip, L square flip, T opposite power rule = quick NEET answer”

🚀 7. Exam Strategy

• Never solve long derivation in NEET
• Always use dimensional formula shortcut
• Save time: 10–15 seconds per question