The correct option is **C. Force**. ### Detailed Explanation In the International System of Units (SI), quantities are classified into two main categories: **base quantities** and **derived quantities**. 1. **Base Quantities**: These are the fundamental physical quantities from which other quantities can be derived. The seven base quantities in the SI system are: - Length (meter, m) - Mass (kilogram, kg) - Time (second, s) - Electric current (ampere, A) - Thermodynamic temperature (kelvin, K) - Amount of substance (mole, mol) - Luminous intensity (candela, cd) 2. **Derived Quantities**: These are quantities that are derived from the base quantities through mathematical relationships. They are expressed in terms of the base quantities. Examples of derived quantities include: - Area (square meters, m²) - Volume (cubic meters, m³) - Speed (meters per second, m/s) - Acceleration (meters per second squared, m/s²) - Force (newton, N) Now, let's focus on the options provided: - **A. Length**: This is a base quantity. It is one of the fundamental measurements in physics and is measured in meters (m). - **B. Mass**: This is also a base quantity. It is measured in kilograms (kg) and is fundamental to the study of matter. - **C. Force**: This is a derived quantity. Force is defined by Newton's second law of motion, which states that force equals mass times acceleration (F = ma). In SI units, force is measured in newtons (N), where 1 N = 1 kg·m/s². This shows that force is derived from the base quantities of mass (kg) and acceleration (m/s²). - **D. Time**: This is another base quantity. It is measured in seconds (s) and is fundamental to the measurement of duration. ### Why the Other Options are Wrong or Weaker - **A. Length**: As mentioned, length is a base quantity, not derived. It serves as a fundamental measurement in physics. - **B. Mass**: Similar to length, mass is a base quantity. It is essential for defining other physical concepts but is not derived from other quantities. - **D. Time**: Time is also a base quantity. It is fundamental to the measurement of events and is not derived from other quantities. ### Formulas and Example Calculations To further illustrate the concept of derived quantities, let’s look at the formula for force: \[ F = m \cdot a \] Where: - \( F \) is the force in newtons (N), - \( m \) is the mass in kilograms (kg), - \( a \) is the acceleration in meters per second squared (m/s²). **Example Calculation**: If an object has a mass of 5 kg and is accelerating at 2 m/s², the force can be calculated as follows: \[ F = 5 \, \text{kg} \cdot 2 \, \text{m/s}^2 = 10 \, \text{N} \] This calculation shows how force (a derived quantity) is dependent on the base quantities of mass and acceleration. ### Common Pitfalls - Confusing base quantities with derived quantities is a common mistake. Remember that base quantities are fundamental and cannot be broken down further, while derived quantities are combinations of base quantities. - Misunderstanding the units of derived quantities can lead to errors in calculations. Always ensure that you are using the correct units when applying formulas. ### Revision Summary - **Base quantities** in SI include length, mass, time, electric current, temperature, amount of substance, and luminous intensity. - **Derived quantities** are formed from base quantities; force is a prime example (F = ma). - **Force** is measured in newtons (N), which is derived from kilograms (kg) and meters per second squared (m/s²). - Always check the definitions and units of quantities to avoid confusion between base and derived quantities.