1) A U-tube, in which both ends are open to the atmosphere, is partially filled with water. Oil which does not mix with water is poured into one side of the tube until it stands a distance d=12.3 mm above the water level on the other side which has meanwhile risen a distancea=67.5 mm from its original level Find the density of the oil
2) The mercury column in a barometer has a measured height h of 740.35 mm. the temperature is-5.0 C
which temperature the density of mercury is 1.3608 104 kg/m3. the free-fall acceleration at the site of the
barometer is 9.7835 m/s2. What is the atmospheric pressure?

1) 916 kg/m³

2) 9.8566×10⁴ Pa

Explanation:

1) Originally, the water is at the same level on both sides.  When the oil is added, one side goes down 67.5 mm and the other side goes up 67.5 mm.  The top of the oil is 12.3 mm above the water, so the total height of the oil relative to the low end of the water is:

12.3 mm + 67.5 mm + 67.5 mm = 147.3 mm

And the height of the water relative to the low end is:

67.5 mm + 67.5 mm = 135 mm

The pressure at the bottom of the oil equals the pressure of the water at the same elevation.

P = P

ρgh = ρgh

ρh = ρh

ρ (147.3 mm) = (1000 kg/m³) (135 mm)

ρ = 916 kg/m³

2) P = ρgh

P = (1.3608×10⁴ kg/m³) (9.7835 m/s²) (0.74035 m)

P = 9.8566×10⁴ Pa

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