Definition check — value of one joule: One joule is numerically equal to which of the following?

Introduction / Context:Knowing exact SI equivalences helps convert between descriptive and formula-based expressions. Engineers frequently toggle between J, N·m, and W·s when analyzing power and energy transfers.

Given Data / Assumptions:

• SI definitions: joule (J), newton (N), meter (m).
• Work W = F * s.

Concept / Approach:By definition, 1 joule is the work done when a force of 1 newton acts through a distance of 1 meter in the direction of the force. Hence 1 J = 1 N·m.

Step-by-Step Solution:Apply definition: W = F*s.Set F = 1 N and s = 1 m in the same direction.Compute W = 1 * 1 = 1 N·m = 1 J.

Verification / Alternative check:Dimensional consistency: 1 J = 1 kg·m^2/s^2, which equals the product of 1 N (kg·m/s^2) and 1 m, confirming 1 N·m.

Why Other Options Are Wrong:

• 0.1 N·m, 10 N·m, 100 N·m: Incorrect scalings; only 1 N·m equals 1 J.

Common Pitfalls:

• Confusing torque (also in N·m) with energy; context matters even though units match.

Final Answer:1 N·m