Unit equivalence via dimensional analysis Steps:

• Express derived units in SI base units: J = kg m² s⁻², N = kg m s⁻², C = A s (A = ampere).
• Option A: J C⁻¹ = (kg m² s⁻²)(A s)⁻¹ = kg m² s⁻³ A⁻¹.
• Option B: J s = (kg m² s⁻²) s = kg m² s⁻¹.
• Option C: N m = (kg m s⁻²) m = kg m² s⁻².
• Compare each to its paired expression; match occurs when bases are identical.

Why C is correct:

• N m equals J by definition (work = force × distance), and J = kg m² s⁻².

Why the others are wrong:

• A: J C⁻¹ introduces A⁻¹ and s⁻³, matching volt, not kg m² s⁻².
• B: J s adds s, yielding kg m² s⁻¹ (action units), not kg m² s⁻².
• D: N matches kg m s⁻², but pairs with force units, not the energy expression kg m² s⁻² shared by A–C.

Final answer: C