Dimensional analysis gives (velocity)ˣ = (pressure difference)³⁄² × (density)⁻³⁄². Find x.
Physics · Mixed Chapter
JEE Main Practice

Question

Dimensional analysis gives (velocity)ˣ = (pressure difference)³⁄² × (density)⁻³⁄². Find x.

G1 Physics · Accepted Answer

Step 1: [ΔP] = ML⁻¹T⁻² and [ρ] = ML⁻³. Step 2: [ΔP/ρ] = L²T⁻². Step 3: (ΔP/ρ)³⁄² has dimensions L³T⁻³ = [velocity]³. Hence x = 3.