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Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 x 10⁻3 N/m, then the diameter of capillary will be
- a)0.1 mm
- b)0.5 mm
- c)1.0 mm
- d)2.0 mm
Correct answer is option 'C'. Can you explain this answer?
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Water rises in a capillary tube when its one end is dipped vertically ...
Given data:
Height of rise, h = 3 cm = 0.03 m
Surface tension, σ = 75 x 10^(-3) N/m
To find: Diameter of capillary tube
Formula used:
The height of rise of a liquid in a capillary tube is given by the formula:
h = (2σ cosθ) / (ρgr)
where,
σ = surface tension of the liquid
θ = contact angle between the liquid and the capillary wall
ρ = density of the liquid
g = acceleration due to gravity
r = radius of the capillary tube
Assumptions made:
1. The capillary tube is vertical.
2. The contact angle between the water and the capillary wall is 0° (since water wets the glass capillary).
Calculation:
From the formula,
r = (2σ cosθ) / (ρgh)
Since θ = 0°,
r = (2σ) / (ρgh)
Substituting the given values,
r = (2 x 75 x 10^(-3) N/m) / [(1000 kg/m³) x (9.8 m/s²) x (0.03 m)]
r = 0.00102 m = 1.02 mm
Therefore, the diameter of the capillary tube is twice the radius, i.e.,
Diameter = 2r = 2 x 1.02 mm = 2.04 mm ≈ 1.0 mm
The correct option is (c) 1.0 mm.
Thus, the diameter of the capillary tube is 1.0 mm.
Height of rise, h = 3 cm = 0.03 m
Surface tension, σ = 75 x 10^(-3) N/m
To find: Diameter of capillary tube
Formula used:
The height of rise of a liquid in a capillary tube is given by the formula:
h = (2σ cosθ) / (ρgr)
where,
σ = surface tension of the liquid
θ = contact angle between the liquid and the capillary wall
ρ = density of the liquid
g = acceleration due to gravity
r = radius of the capillary tube
Assumptions made:
1. The capillary tube is vertical.
2. The contact angle between the water and the capillary wall is 0° (since water wets the glass capillary).
Calculation:
From the formula,
r = (2σ cosθ) / (ρgh)
Since θ = 0°,
r = (2σ) / (ρgh)
Substituting the given values,
r = (2 x 75 x 10^(-3) N/m) / [(1000 kg/m³) x (9.8 m/s²) x (0.03 m)]
r = 0.00102 m = 1.02 mm
Therefore, the diameter of the capillary tube is twice the radius, i.e.,
Diameter = 2r = 2 x 1.02 mm = 2.04 mm ≈ 1.0 mm
The correct option is (c) 1.0 mm.
Thus, the diameter of the capillary tube is 1.0 mm.
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Water rises in a capillary tube when its one end is dipped vertically ...
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Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 x 103 N/m, then the diameter of capillary will bea)0.1 mmb)0.5 mmc)1.0 mmd)2.0 mmCorrect answer is option 'C'. Can you explain this answer?
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Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 x 103 N/m, then the diameter of capillary will bea)0.1 mmb)0.5 mmc)1.0 mmd)2.0 mmCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 x 103 N/m, then the diameter of capillary will bea)0.1 mmb)0.5 mmc)1.0 mmd)2.0 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 x 103 N/m, then the diameter of capillary will bea)0.1 mmb)0.5 mmc)1.0 mmd)2.0 mmCorrect answer is option 'C'. Can you explain this answer?.
Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 x 103 N/m, then the diameter of capillary will bea)0.1 mmb)0.5 mmc)1.0 mmd)2.0 mmCorrect answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 x 103 N/m, then the diameter of capillary will bea)0.1 mmb)0.5 mmc)1.0 mmd)2.0 mmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water rises in a capillary tube when its one end is dipped vertically in it, is 3 cm. If the surface tension of water is 75 x 103 N/m, then the diameter of capillary will bea)0.1 mmb)0.5 mmc)1.0 mmd)2.0 mmCorrect answer is option 'C'. Can you explain this answer?.
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