A U-tube open to air contains water. Immiscible oil is poured into one arm until its free surface stands 10 mm above the final water level in the other arm. The water level in the right arm rises 65 mm above its original level, and the left water level drops 65 mm. Find oil density, given ρwater = 1000 kg/m³. [Image]
Options

Question

A U-tube open to air contains water. Immiscible oil is poured into one arm until its free surface stands 10 mm above the final water level in the other arm. The water level in the right arm rises 65 mm above its original level, and the left water level drops 65 mm. Find oil density, given ρwater = 1000 kg/m³. [Image]

Options

G1 Physics · Accepted Answer

Step 1: Water rises 65 mm on the right and falls 65 mm on the left; the separation of the two water levels is 130 mm. Step 2: The oil free surface is 10 mm above the final right-hand water level. Step 3: Oil-column height above the interface = 130 + 10 = 140 mm. Step 4: Equate pressures at the same horizontal level in the two arms: ρoil g(140 mm) = ρwater g(130 mm). Step 5: ρoil = 1000 × 130/140 ≈ 928.57 kg/m³. Final answer: approximately 928 kg/m³ (Option C).