Which of the following physical quantities has the same dimensional formula as that of pressure?
A. Energy per unit volume
B. Momentum per unit area
C. Power per unit volume
D. Force per unit length
Answer: Option A
Solution (By JKExamLibrary)
Pressure has dimensions [ML⁻¹T⁻²]. Energy per unit volume: Energy is [ML²T⁻²], volume is [L³], so [ML²T⁻²]/[L³] = [ML⁻¹T⁻²], matching pressure. Force per unit length is [MLT⁻²]/[L] = [MT⁻²]. Momentum per unit area is [MLT⁻¹]/[L²] = [ML⁻¹T⁻¹]. Power per unit volume is [ML²T⁻³]/[L³] = [ML⁻¹T⁻³]. This dimensional equivalence explains why pressure appears in Bernoulli's equation alongside energy density. Memory aid: Pressure and energy density both represent stored energy per spatial dimension.
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