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A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.?
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Given:
- Density of mercury (Hg) = 13.6 g/cm^3
- Density of glycerine = 1.3 g/cm^3
- Density of oil = 0.8 g/cm^3
- Length of glycerine column = 10 cm
To find:
Length of oil column
Approach:
1. Since the U-tube is in vertical position, the pressure at the same horizontal level on both arms of the U-tube is the same.
2. We can use the concept of pressure to find the length of the oil column.
Solution:
1. Let's assume the length of the oil column as 'x' cm.
2. The pressure at the same horizontal level in the mercury arm is the same as the pressure in the glycerine and oil arm.
3. The pressure at a certain depth in a fluid is given by the formula:
Pressure = Density × g × height
where g is the acceleration due to gravity (9.8 m/s^2).
4. Let's calculate the pressure in each arm:
- In the mercury arm: Pressure = Density of Hg × g × height
- In the glycerine arm: Pressure = Density of glycerine × g × height
- In the oil arm: Pressure = Density of oil × g × height
5. Since the pressure is the same in all arms at the same horizontal level, we can equate the pressures:
Density of Hg × g × height = Density of glycerine × g × height + Density of oil × g × x
6. Simplifying the equation:
Density of Hg × height = Density of glycerine × height + Density of oil × x
7. Substituting the given values:
13.6 × height = 1.3 × height + 0.8 × x
8. Solving for x:
13.6 × height - 1.3 × height = 0.8 × x
12.3 × height = 0.8 × x
x = (12.3 × height) / 0.8
9. Substituting the value of height as 10 cm:
x = (12.3 × 10) / 0.8
x ≈ 153.75 cm ≈ 9.6 cm (rounded to one decimal place)
Answer:
The length of the oil column is approximately 9.6 cm.
- Density of mercury (Hg) = 13.6 g/cm^3
- Density of glycerine = 1.3 g/cm^3
- Density of oil = 0.8 g/cm^3
- Length of glycerine column = 10 cm
To find:
Length of oil column
Approach:
1. Since the U-tube is in vertical position, the pressure at the same horizontal level on both arms of the U-tube is the same.
2. We can use the concept of pressure to find the length of the oil column.
Solution:
1. Let's assume the length of the oil column as 'x' cm.
2. The pressure at the same horizontal level in the mercury arm is the same as the pressure in the glycerine and oil arm.
3. The pressure at a certain depth in a fluid is given by the formula:
Pressure = Density × g × height
where g is the acceleration due to gravity (9.8 m/s^2).
4. Let's calculate the pressure in each arm:
- In the mercury arm: Pressure = Density of Hg × g × height
- In the glycerine arm: Pressure = Density of glycerine × g × height
- In the oil arm: Pressure = Density of oil × g × height
5. Since the pressure is the same in all arms at the same horizontal level, we can equate the pressures:
Density of Hg × g × height = Density of glycerine × g × height + Density of oil × g × x
6. Simplifying the equation:
Density of Hg × height = Density of glycerine × height + Density of oil × x
7. Substituting the given values:
13.6 × height = 1.3 × height + 0.8 × x
8. Solving for x:
13.6 × height - 1.3 × height = 0.8 × x
12.3 × height = 0.8 × x
x = (12.3 × height) / 0.8
9. Substituting the value of height as 10 cm:
x = (12.3 × 10) / 0.8
x ≈ 153.75 cm ≈ 9.6 cm (rounded to one decimal place)
Answer:
The length of the oil column is approximately 9.6 cm.
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A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.?
Question Description
A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.?.
A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.?.
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A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.?, a detailed solution for A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.? has been provided alongside types of A vertical U-tube of uniform cross section contains mercury in both sides of its arms. A glycerine column of length 10cm is introduced into one of its arms. Oil of density 0.8g/cm^3 is poured into other arm until the upper surface of the oil and glycerine are in the same horizontal level. Find the length of oil column. Density of Hg=13.6g/cm^3 Density of glycerine =1.3g/cm^3. Ans.9.6 cm.? theory, EduRev gives you an
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