Liquids with densities ρ₁ and ρ₂ (g/cm³) give mixture density 4 when mixed in equal volumes and mixture density 3 when mixed in equal masses. Find ρ₁.
Physics · Mixed Chapter
JEE Main Practice

Question

Liquids with densities ρ₁ and ρ₂ (g/cm³) give mixture density 4 when mixed in equal volumes and mixture density 3 when mixed in equal masses. Find ρ₁.

G1 Physics · Accepted Answer

Step 1: Equal volumes give (ρ₁+ρ₂)/2=4 ⇒ρ₁+ρ₂=8. Step 2: Equal masses give mixture density 2ρ₁ρ₂/(ρ₁+ρ₂)=3 ⇒ρ₁ρ₂=12. Step 3: Solve t²−8t+12=0 ⇒(t−6)(t−2)=0. The two densities are 6 and 2 g/cm³. Step 4: Without specifying which liquid is labelled 1, both ρ₁=6 and ρ₁=2 are possible. The source selects ρ₁=6.