Verifying SI unit equivalences via dimensional analysis

Steps:

• Nm = N·m, where N = kg·m·s⁻², so Nm = kg·m²·s⁻².
• Ns = N·s = (kg·m·s⁻²)·s = kg·m·s⁻¹, equivalent to kg·m/s.
• Js = J·s, where J = N·m = kg·m²·s⁻², so Js = kg·m²·s⁻¹, equivalent to kg·m²/s.
• Pa = N/m² = (kg·m·s⁻²)/m² = kg·m⁻¹·s⁻²; kg·m·s² = kg·m·s², not equivalent due to mismatched exponents for m and s.

Why D is correct:

• Pa defines pressure as force per unit area (kg·m⁻¹·s⁻²), but kg·m·s² represents mass times length times time squared, with opposite signs for length and time exponents.

Why the others are wrong:

• A: Nm expands directly to kg·m²·s⁻², matching the given base units.
• B: Ns expands to kg·m·s⁻¹, identical to kg·m/s.
• C: Js expands to kg·m²·s⁻¹, identical to kg·m²/s.

Final answer: D