Dimensional analysis: Derived units are formed from combinations of which fundamental elements?

Introduction / Context:The SI system organizes measurements into seven fundamental units (meter, kilogram, second, ampere, kelvin, mole, candela). Many engineering quantities—such as force, energy, voltage, and resistance—are not fundamental; they are derived from these base units by algebraic combination.

Given Data / Assumptions:

• Derived units include newton (N), joule (J), volt (V), ohm (Ω), etc.
• We are concerned with how such units originate.
• Metric prefixes are scale factors, not new base quantities.

Concept / Approach:Derived units follow from physical laws. For example, force = mass * acceleration → N = kg * m / s^2. Voltage = power/current and power = energy/time → V = J/C and J = N * m, etc. Thus, all derived units reduce to products and ratios of the fundamental SI units, sometimes with special names for convenience.

Step-by-Step Solution:

Verification / Alternative check:Dimensional homogeneity in equations confirms correctness; every term reduces to the same base-unit combination, reinforcing the idea that derived units come from fundamentals.

Why Other Options Are Wrong:

• Electrical quantities: These may themselves be derived (e.g., volt, ohm).
• Metric prefixes: Only scale units; they do not define new physical dimensions.
• International standards: Governance and naming, not dimensional construction.

Common Pitfalls:Confusing convenience names (e.g., tesla) with base units or thinking prefixes like kilo create new dimensions—they only rescale existing ones.

Final Answer:fundamental units