Complete Study Material for JEE, NEET, CBSE Board Class 11 Exams
Q: What are Fundamental Quantities?
A: Fundamental quantities are physical quantities that are independent and do not require other quantities for their definition. They are also known as absolute or base quantities. Examples include length, mass, and time.
Q: What are derived quantities?
A: Derived quantities are those that can be obtained through suitable multiplication or division of fundamental quantities. For example, area and volume are derived from length.
Examples of Fundamental and Derived Quantities
- Fundamental Quantities: Length, Mass, Time
- Derived Quantities: Area (Length²), Volume (Length³), Speed (Length/Time), Force (Mass × Acceleration)
Note: The choice of fundamental quantities in mechanics is arbitrary. If speed and time are chosen as fundamental, length becomes derived as Speed × Time. Similarly, if force and acceleration are fundamental, mass becomes derived as Force / Acceleration.
Fundamental and Derived Units
Q: What are fundamental units?
A: Fundamental units are the standard units for fundamental quantities. In mechanics, units of mass, length, and time are considered fundamental. Examples: Kilogram (kg), Meter (m), Second (s).
Q: What are derived units?
A: Derived units are expressed in terms of fundamental units. Examples include:
- Speed (m/s) → Derived from Length/Time
- Force (kg·m/s²) → Derived from Mass × Acceleration
- Density (kg/m³) → Derived from Mass/Volume
Examples of Fundamental and Derived Units
- Fundamental Units: Meter (m), Kilogram (kg), Second (s)
- Derived Units: m² (Area), m³ (Volume), m/s (Speed), kg·m/s² (Force)
Multiple Choice Questions (MCQs) with Answers & Explanations
Q1: Which of the following is a fundamental quantity?
A) Speed
B) Force
C) Mass
D) Acceleration
Answer: C) Mass
Explanation: Mass is independent and does not rely on other quantities, making it fundamental.
Q2: Which of the following is a derived quantity?
A) Length
B) Time
C) Force
D) Mass
Answer: C) Force
Explanation: Force is derived from the equation Force = Mass × Acceleration, making it a derived quantity.
Q3: The unit of force in the SI system is:
A) kg/m³
B) m/s
C) kg·m/s²
D) s⁻¹
Answer: C) kg·m/s²
Explanation: Force is given by F = Mass × Acceleration, and its SI unit is Newton (N) = kg·m/s².
Q4: If force and acceleration are chosen as fundamental, which quantity becomes derived?
A) Length
B) Mass
C) Speed
D) Time
Answer: B) Mass
Explanation: Mass is expressed as Force / Acceleration, making it a derived quantity in this case.
Q5: The SI unit of speed is:
A) m/s²
B) m/s
C) kg·m/s²
D) m³
Answer: B) m/s
Explanation: Speed is defined as Distance / Time, and its SI unit is meters per second (m/s).
Worksheet on Fundamental and Derived Quantities
Q1: Define fundamental and derived quantities with two examples each.
Q2: Explain why length, mass, and time are chosen as fundamental quantities in mechanics.
Q3: How can speed and time be chosen as fundamental quantities?
Q4: Classify the following as fundamental or derived quantities:
- Energy
- Temperature
- Work
- Density
Frequently Asked Questions (FAQs)
Q1: Why are fundamental quantities important?
A: Fundamental quantities are the basis for defining all other physical quantities. Without them, measurements and scientific equations would not be standardized.
Q2: Can fundamental quantities change?
A: The choice of fundamental quantities is arbitrary and can change based on the system of units. However, in mechanics, mass, length, and time are the standard fundamental quantities.
Q3: What is an example of a fundamental and derived unit?
A: The meter (m) is a fundamental unit (for length), whereas m² (square meter) is a derived unit (for area).
Q4: Is acceleration a fundamental or derived quantity?
A: Acceleration is a derived quantity, as it is expressed as Velocity / Time (m/s²).
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