In S.I. terminology, the joule (J) equals newton–metre (Nm). Identify the physical quantities for which these units are used in practice, noting the conventional use for torque as well.

Introduction / Context:In S.I., work and energy share the unit joule (J). Since 1 J = 1 Nm, the same dimensional product appears in torque calculations. However, conventionally engineers write torque in Nm (not J) to distinguish the vectorial, moment-like nature of torque from scalar energy or work, even though the dimensions match.

Given Data / Assumptions:

• Work and energy are scalars measured in joules.
• Torque (moment of force) is a vector (or axial vector) commonly expressed as Nm.
• 1 J = 1 Nm in S.I. dimensional terms.

Concept / Approach:

Use the work definition W = F * s (component along displacement) and torque definition M = F * d (perpendicular distance). Both are force times distance, but they represent different physical concepts. Hence, the shared unit does not imply identical physical meaning.

Step-by-Step Solution:

Verification / Alternative check:

Dimensional analysis: N = kgm/s^2, so Nm = kgm^2/s^2. This dimension appears in both torque and energy computations, confirming the equivalence of units despite different physical interpretations.

Why Other Options Are Wrong:

• Only work and energy: Excludes torque, which also uses Nm in practice.

Common Pitfalls:

• Interchanging 'joule' with torque values in reports; best practice labels torque explicitly as Nm.
• Forgetting that torque’s direction depends on the right-hand rule, unlike scalar energy.

Final Answer:

All the above.