Question

150. A U tube with both ends open to the atmosphere, ispartially filled with water. Oil, which is immiscible withwater, is poured into one side until it stands at adistance of 10 mm above the water level on the otherside. Meanwhile the water rises by 65 mm from itsoriginal level (see diagram). The density of the oil is:
(1) 650 kg m⁻³
(2) 425 kg m⁻³
(3) 800 kg m⁻³
(4) 928 kg m⁻³

Answer 1

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Answer 2

Thus the density of the oil is ρ oil =928 kgm^-3

Explanation:

Gauge pressure is defined as:

Pressure difference  between hydro-static and atmospheric pressure

where

P - Po =  ρgh

P - Po =  gauge pressure

Pressure of two points lie in the same horizontal level should be same and P=  ρgh

Both ends of tube is open, so the pressure on both the free surface must be equal.

P1 =P2

=> h oil x ρoil x g = h water.ρwater.g

ρoil = h water} . ρwater / h oil

ρoil = (65 + 65) x 1000 / 65+65+10

ρ oil =928 kg.m^-3

Thus the density of the oil is ρ oil =928 kg.m^-3