**Correct Option: C. Force** ### Explanation of Why the Answer is Correct 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 not fundamental but are essential for describing physical phenomena. **Force** is a classic example of a derived quantity. It is defined by Newton's second law of motion, which states that force is the product of mass and acceleration. The formula for force (F) is given by: \[ F = m \cdot a \] Where: - \( F \) is the force measured in newtons (N), - \( m \) is the mass measured in kilograms (kg), - \( a \) is the acceleration measured in meters per second squared (m/s²). From this formula, we can see that force is derived from the base quantities of mass and length (since acceleration is derived from the change in velocity, which involves length and time). Therefore, the SI unit of force, the newton (N), can be expressed in terms of base units as: \[ 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \] This shows that force is indeed a derived quantity. ### Explanation of Why the Other Options are Wrong or Weaker - **A. Length**: Length is a base quantity in the SI system. It is measured in meters (m) and does not depend on any other quantities for its definition. Therefore, it is not a derived quantity. - **B. Mass**: Mass is also a base quantity in the SI system, measured in kilograms (kg). Like length, it is fundamental and does not derive from other quantities. Thus, it is not a derived quantity. - **D. Time**: Time is another base quantity in the SI system, measured in seconds (s). It is fundamental and serves as a basis for other derived quantities, such as velocity and acceleration. Therefore, it is not a derived quantity. ### Summary of Key Points - **Derived Quantity**: Force is a derived quantity in the SI system, defined as the product of mass and acceleration. - **Base Quantities**: Length, mass, and time are all base quantities in the SI system and do not derive from other quantities. - **Formula for Force**: \( F = m \cdot a \) (where \( F \) is force, \( m \) is mass, and \( a \) is acceleration). - **Unit of Force**: The SI unit of force is the newton (N), which can be expressed as \( 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \). This understanding of base and derived quantities is crucial for solving problems in physics and for understanding the relationships between different physical concepts.