Units and dimensions — selecting the S.I. unit of energy: Which of the following is the correct S.I. (International System) unit for energy?

Introduction / Context:
Dimensional consistency and correct units are crucial in engineering calculations. Energy appears across mechanics, heat transfer, and electricity; selecting the correct S.I. unit prevents cascading errors in analyses and designs.

Given Data / Assumptions:

• S.I. base units and derived units are used.
• Energy may be mechanical (work), thermal (heat), or electrical in form.
• Power and force units are related but distinct from energy.

Concept / Approach:
In S.I., the unit of energy (and work) is the joule, defined as 1 J = 1 N·m. The watt (W) is power, equal to J/s. Compound variants such as J/m or J·m represent line energy density or energy times length and are not standard units for energy alone.

Step-by-Step Solution:
Recall: energy (work) W = force * displacement ⇒ unit = N·m.By definition, 1 N = 1 kg·m/s^2 ⇒ N·m has dimensions kg·m^2/s^2, named the joule (J).Therefore, the correct S.I. unit is Joule (J).

Verification / Alternative check:
Electrical energy from power P integrated over time t yields E = P * t with units W·s = J, confirming consistency across domains.

Why Other Options Are Wrong:
J·m is energy multiplied by length (not energy). W is power (rate of energy). J/m is energy per length (a density), not energy itself.

Common Pitfalls:
Interchanging power and energy; forgetting that torque also uses N·m but is not energy (axial moment), despite sharing units.

Final Answer:
Joule (J)