⚖️ Class 11 Physics – Units and Measurement

🌍 Introduction: Physics is a quantitative science, meaning all observations in nature must be measured and expressed with proper units. This chapter “Units and Measurements” (Class 11 Physics) is important for Board Exams and NEET Physics as it forms the foundation for all further study.

✨ Physical Quantities

• Any quantity that can be measured is called a physical quantity.
• A physical quantity is expressed as:
  Physical Quantity = Magnitude + Unit
  Example: Length = 5 m (5 = magnitude, m = unit).

🔹 Systems of Units

1. CGS System → centimetre, gram, second
2. MKS System → metre, kilogram, second
3. FPS System → foot, pound, second
4. SI System → Internationally accepted system (adopted in 1960).

🔹 SI Base Quantities (7)

Fundamental Quantity	Unit	Symbol
Length	metre	m
Mass	kilogram	kg
Time	second	s
Electric current	ampere	A
Temperature	kelvin	K
Amount of substance	mole	mol
Luminous intensity	candela	cd

👉Derived units (e.g., velocity, force, energy) are expressed in terms of these base units.

🔹 Significant Figures

• Indicate the precision of measurement.
• Rules:
  
• All non-zero digits are significant.
• Zeros between non-zero digits are significant.
• Leading zeros are NOT significant.
• Trailing zeros are significant only after decimal.
• Example: 0.004560 has 4 significant figures.

🔹 Dimensions of Physical Quantities

What are Dimensions?

• Dimensions show how a physical quantity depends on fundamental quantities.
• Represented as:
  [M^a L^b T^c ]

Examples

1. Velocity → [M^0 L^1 T^{-1}]
2. Acceleration → [M^0 L^1 T^{-2}]
3. Force → [M^1 L^1 T^{-2}]
4. Work/Energy → [M^1 L^2 T^{-2}]
5. Pressure → [M^1 L^{-1} T^{-2}]

📌 Applications of Dimensional Analysis

1. To check correctness of equations
   Example: v² = u² + 2as (LHS dimensions = RHS dimensions), hence correct.
2. To derive relations between physical quantities
   Example: Time period of a pendulum T ∝ √(L/g)
3. To convert units
   Example: 1 erg = 10^{-7} joule (from dimensional method).

⚠️ Limitations

• Cannot give dimensionless constants (π, sinθ, etc.).
• Only checks correctness in form, not in value.

📑 Important Questions (Class 11)

Q1. Define fundamental and derived units with examples.

Q2. Write the dimensional formula of work, energy and power.

Q3. State two applications of dimensional analysis.

Q4. Give limitations of dimensional analysis.

Q5. Write the dimensional formula of pressure.

🧾 NEET Previous Year MCQs

Q1. The dimensional formula of Power is:

a) [M L^2 T^{-3}]

b) [M L T^{-2}]

c) [M L^2 T^{-2}]

d) [M L^2 T^{-1}]

👉 Answer: (a) [M L² T⁻³]

Q2. Which is not a fundamental unit?

a) Second

b) Kilogram

c) Newton

d) Mole

👉 Answer: (c) Newton

Q3. The dimensional formula of Pressure is:

a) [M L^0 T^{-2}]

b) [M L^{-1} T^{-2}]

c) [M L T^{-2}]

d) [M^0 L^2 T^{-2}]

👉 Answer: (b) [M L⁻¹ T⁻²]

📌 Summary for Students

• Units are necessary to measure physical quantities.
• SI system has 7 fundamental units and many derived units.
• Dimensional analysis is useful but has limitations.
• Dimensions help check equations and derive relations.

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