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A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = 1.3 g/
) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/
is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm?
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A vertical U-tube of uniform inner cross section contains mercury in b...
Given data:
- Density of glycerin, ρglycerin = 1.3 g/cm3
- Length of glycerin column, h = 10 cm
- Density of oil, ρoil = 0.8 g/cm3
- Density of mercury, ρmercury = 13.6 g/cm3

Analysis:
- Let the length of the oil column be H cm.
- The pressure at the liquid interface is the same in both arms of the U-tube.
- The pressure at the interface can be calculated as follows:
P = P0 + ρgh

Calculations:
- In the arm containing glycerin:
P = P0 + ρmercurygh
P = P0 + 13.6 * 10 * 9.8
P = P0 + 1332.8
- In the arm containing oil:
P = P0 + ρmercurygh + ρglyceringh
P = P0 + 13.6 * H * 9.8 + 1.3 * 10 * 9.8
P = P0 + 133.6H + 127.4
- Since the pressures at the liquid interface are the same:
P0 + 1332.8 = P0 + 133.6H + 127.4
1332.8 = 133.6H + 127.4
H = (1332.8 - 127.4) / 133.6
H = 5.4 / 133.6
H ≈ 0.04 cm

Conclusion:
- The length of the oil column is approximately 0.04 cm.
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A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = 1.3 g/) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm?
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A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = 1.3 g/) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = 1.3 g/) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertical U-tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = 1.3 g/) column of length 10 cm is introduced into one of its arms. Oil of density 0.8 gm/ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column, Density of mercury = 13.6 g/cm?.
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