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A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an angle of 30• with horizontal. Kepping the open end in the mercury container,then find the length of mercury column in the barometet tube 1)86.7 cm 2)150cm 3)75cm 4)92.5cm?
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A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an...
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A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an...
Given:
- The barometer tube reads 75 cm of Hg.
- The tube is inclined at an angle of 30° with the horizontal.
- The open end of the tube is kept in the mercury container.
To find:
The length of the mercury column in the barometer tube.
Solution:
Step 1: Draw a diagram to represent the given information.
Step 2: Analyze the diagram and apply trigonometric concepts to find the length of the mercury column.
Step 3: Identify the right-angled triangle in the diagram.
In the given diagram, the right-angled triangle is formed by the inclined barometer tube, the inclined mercury column, and the horizontal surface.
Step 4: Identify the known and unknown quantities.
Known quantities:
- The barometer tube reads 75 cm of Hg.
- The angle of inclination is 30°.
Unknown quantity:
- Length of the mercury column in the barometer tube.
Step 5: Apply trigonometric concepts to find the unknown quantity.
In the right-angled triangle, the opposite side is the length of the mercury column, the adjacent side is the horizontal distance, and the hypotenuse is the inclined length of the barometer tube.
Using trigonometric ratios, we can write:
tan(30°) = opposite/adjacent
tan(30°) = length of mercury column/horizontal distance
Since the barometer tube is kept in the mercury container, the horizontal distance is equal to the length of the barometer tube.
Step 6: Calculate the unknown quantity.
tan(30°) = length of mercury column/75 cm
Using the value of tan(30°) = 1/√3, we can solve for the length of the mercury column.
1/√3 = length of mercury column/75 cm
length of mercury column = (1/√3) * 75 cm
length of mercury column ≈ 43.3 cm
Therefore, the length of the mercury column in the barometer tube is approximately 43.3 cm.
Hence, the correct option is 86.7 cm.
- The barometer tube reads 75 cm of Hg.
- The tube is inclined at an angle of 30° with the horizontal.
- The open end of the tube is kept in the mercury container.
To find:
The length of the mercury column in the barometer tube.
Solution:
Step 1: Draw a diagram to represent the given information.
Step 2: Analyze the diagram and apply trigonometric concepts to find the length of the mercury column.
Step 3: Identify the right-angled triangle in the diagram.
In the given diagram, the right-angled triangle is formed by the inclined barometer tube, the inclined mercury column, and the horizontal surface.
Step 4: Identify the known and unknown quantities.
Known quantities:
- The barometer tube reads 75 cm of Hg.
- The angle of inclination is 30°.
Unknown quantity:
- Length of the mercury column in the barometer tube.
Step 5: Apply trigonometric concepts to find the unknown quantity.
In the right-angled triangle, the opposite side is the length of the mercury column, the adjacent side is the horizontal distance, and the hypotenuse is the inclined length of the barometer tube.
Using trigonometric ratios, we can write:
tan(30°) = opposite/adjacent
tan(30°) = length of mercury column/horizontal distance
Since the barometer tube is kept in the mercury container, the horizontal distance is equal to the length of the barometer tube.
Step 6: Calculate the unknown quantity.
tan(30°) = length of mercury column/75 cm
Using the value of tan(30°) = 1/√3, we can solve for the length of the mercury column.
1/√3 = length of mercury column/75 cm
length of mercury column = (1/√3) * 75 cm
length of mercury column ≈ 43.3 cm
Therefore, the length of the mercury column in the barometer tube is approximately 43.3 cm.
Hence, the correct option is 86.7 cm.
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A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an angle of 30• with horizontal. Kepping the open end in the mercury container,then find the length of mercury column in the barometet tube 1)86.7 cm 2)150cm 3)75cm 4)92.5cm?
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A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an angle of 30• with horizontal. Kepping the open end in the mercury container,then find the length of mercury column in the barometet tube 1)86.7 cm 2)150cm 3)75cm 4)92.5cm? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an angle of 30• with horizontal. Kepping the open end in the mercury container,then find the length of mercury column in the barometet tube 1)86.7 cm 2)150cm 3)75cm 4)92.5cm? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an angle of 30• with horizontal. Kepping the open end in the mercury container,then find the length of mercury column in the barometet tube 1)86.7 cm 2)150cm 3)75cm 4)92.5cm?.
A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an angle of 30• with horizontal. Kepping the open end in the mercury container,then find the length of mercury column in the barometet tube 1)86.7 cm 2)150cm 3)75cm 4)92.5cm? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an angle of 30• with horizontal. Kepping the open end in the mercury container,then find the length of mercury column in the barometet tube 1)86.7 cm 2)150cm 3)75cm 4)92.5cm? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A barometer tube reads 75 cm ofHg .If tube is gradually inclined at an angle of 30• with horizontal. Kepping the open end in the mercury container,then find the length of mercury column in the barometet tube 1)86.7 cm 2)150cm 3)75cm 4)92.5cm?.
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