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Which of the following expressions has the same dimensions as pressure?

1. Momentum per unit volume
2. Momentum per unit volume per unit energy
3. Energy per unit volume
4. Force per unit length

Correct answer: Energy per unit volume

Solution

Pressure dimensions: [M L⁻¹ T⁻²]. Momentum per unit volume: [M L T⁻¹] / [L³] = [M L⁻² T⁻¹] — not pressure. Momentum per unit volume per energy: [M L⁻² T⁻¹] / [M L² T⁻²] = [M⁰ L⁻⁴ T] — not pressure. Energy per unit volume: [M L² T⁻²] / [L³] = [M L⁻¹ T⁻²] — same as pressure. Force per unit length: [M L T⁻²] / [L] = [M T⁻²] — not pressure. Answer: Energy per unit volume.

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