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When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3?
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When a Fortins barometer is used to measure the pressure on the surfac...
Problem: Calculate the height of a building using a Fortins barometer, given that the main scale readings on the surface of the earth and on the top of the building are the same and the vernier scale readings are 9 and 0, respectively.
Given:
- One M.S.D. = 1 mm
- Number of vernier scale divisions = 10
- Average density of air = 1.3 kg/m3
- Density of mercury = 13.6 g/cm3
Solution:
Step 1: Calculate the pressure difference between the top of the building and the surface of the earth
- The pressure difference can be calculated using the formula:
ΔP = ρgh
where ΔP is the pressure difference, ρ is the density of the fluid (mercury), g is the acceleration due to gravity, and h is the height difference between the top of the building and the surface of the earth.
- Substituting the given values, we get:
ΔP = (13.6 g/cm3) x (9.81 m/s2) x h
ΔP = 133.416 h Pa
Step 2: Calculate the least count of the Fortins barometer
- The least count of the Fortins barometer can be calculated using the formula:
L.C. = 1 M.S.D. / Number of Vernier scale divisions
L.C. = 1 mm / 10
L.C. = 0.1 mm
Step 3: Calculate the difference between the main scale reading and the vernier scale reading
- The difference can be calculated by adding the main scale reading and the vernier scale reading multiplied by the least count.
Difference = Main scale reading + (Vernier scale reading x L.C.)
Difference = Main scale reading + (9 x 0.1 mm)
Difference = Main scale reading + 0.9 mm
Step 4: Calculate the pressure at the top of the building
- The pressure at the top of the building can be calculated by adding the pressure at the surface of the earth to the pressure difference calculated in Step 1.
P2 = P1 + ΔP
P2 = Main scale reading + Difference + ΔP
Step 5: Calculate the height of the building
- The height of the building can be calculated using the formula:
h = (P2 - P1) / (ρg)
where h is the height difference between the top of the building and the surface of the earth, P1 is the pressure at the surface of the earth, P2 is the pressure at the top of the building, ρ is the density of air, and g is the acceleration due to gravity.
- Substituting the values calculated in Steps 1, 4 and the given value for density of air, we get:
h = (Main scale reading + Difference + ΔP - Main scale reading) / (ρg)
h = (0.9 mm + ΔP) / (ρg)
h = (0.9 mm + 133.416 h Pa
Given:
- One M.S.D. = 1 mm
- Number of vernier scale divisions = 10
- Average density of air = 1.3 kg/m3
- Density of mercury = 13.6 g/cm3
Solution:
Step 1: Calculate the pressure difference between the top of the building and the surface of the earth
- The pressure difference can be calculated using the formula:
ΔP = ρgh
where ΔP is the pressure difference, ρ is the density of the fluid (mercury), g is the acceleration due to gravity, and h is the height difference between the top of the building and the surface of the earth.
- Substituting the given values, we get:
ΔP = (13.6 g/cm3) x (9.81 m/s2) x h
ΔP = 133.416 h Pa
Step 2: Calculate the least count of the Fortins barometer
- The least count of the Fortins barometer can be calculated using the formula:
L.C. = 1 M.S.D. / Number of Vernier scale divisions
L.C. = 1 mm / 10
L.C. = 0.1 mm
Step 3: Calculate the difference between the main scale reading and the vernier scale reading
- The difference can be calculated by adding the main scale reading and the vernier scale reading multiplied by the least count.
Difference = Main scale reading + (Vernier scale reading x L.C.)
Difference = Main scale reading + (9 x 0.1 mm)
Difference = Main scale reading + 0.9 mm
Step 4: Calculate the pressure at the top of the building
- The pressure at the top of the building can be calculated by adding the pressure at the surface of the earth to the pressure difference calculated in Step 1.
P2 = P1 + ΔP
P2 = Main scale reading + Difference + ΔP
Step 5: Calculate the height of the building
- The height of the building can be calculated using the formula:
h = (P2 - P1) / (ρg)
where h is the height difference between the top of the building and the surface of the earth, P1 is the pressure at the surface of the earth, P2 is the pressure at the top of the building, ρ is the density of air, and g is the acceleration due to gravity.
- Substituting the values calculated in Steps 1, 4 and the given value for density of air, we get:
h = (Main scale reading + Difference + ΔP - Main scale reading) / (ρg)
h = (0.9 mm + ΔP) / (ρg)
h = (0.9 mm + 133.416 h Pa
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When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3?
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When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3?.
When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3?.
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When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3?, a detailed solution for When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3? has been provided alongside types of When a Fortins barometer is used to measure the pressure on the surface of the earth and on the top of a building the main scale redaing is found to be the same and the vernier scale reading is found to be 9 and zero, respectively. If one M.S.D. is 1 mm and number of vernier scale divisions is 10, calculate the height of the building. Take the average density of air as 1.3kg/m3, and that of mercury as 13.6g/cm3? theory, EduRev gives you an
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