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A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :
- a)10.0 g
- b)20.0 g
- c)2.5 g
- d)5.0 g
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A capillary tube of radius r is immersed in water and water rises in i...
= m = ρ × volume = ρ × h × pr2 = = 5 gm
r’ = 2r
= ρ × hpr2 × 2 = 10 gm
Most Upvoted Answer
A capillary tube of radius r is immersed in water and water rises in i...
Given: radius of first capillary tube = r, height of water in it = h, mass of water in it = 5g
To find: mass of water that will rise in the second capillary tube of radius 2r
Assumption: Both capillary tubes are made of the same material
Formula used: Surface tension = (density of liquid) x (acceleration due to gravity) x (height of liquid column) / (2 x radius of capillary tube)
1. Find the surface tension of water using the given data:
Surface tension = (density of water) x (acceleration due to gravity) x (height of water column) / (2 x radius of first capillary tube)
Density of water = 1000 kg/m³
Acceleration due to gravity = 9.8 m/s²
Height of water column = h
Radius of first capillary tube = r
Surface tension = (1000 x 9.8 x h) / (2 x r)
2. Use the surface tension to find the height of water column that will rise in the second capillary tube:
Surface tension = (density of water) x (acceleration due to gravity) x (height of water column) / (2 x radius of second capillary tube)
Density of water = 1000 kg/m³
Acceleration due to gravity = 9.8 m/s²
Radius of second capillary tube = 2r
Height of water column = (2 x surface tension x radius of second capillary tube) / (density of water x acceleration due to gravity)
Height of water column = (2 x ((1000 x 9.8 x h) / (2 x r)) x 2r) / (1000 x 9.8)
Height of water column = 4h
3. Find the mass of water that will rise in the second capillary tube:
Mass of water = (density of water) x (volume of water)
Volume of water = (pi x (radius of second capillary tube)² x height of water column)
Volume of water = (pi x (2r)² x 4h)
Volume of water = 16(pi x r² x h)
Mass of water = 1000 x 16(pi x r² x h)
Mass of water = 16000(pi x r² x h)
Substituting h = 5g / (pi x r²) in the above equation, we get:
Mass of water = 16000(pi x r² x (5g / (pi x r²)))
Mass of water = 80000g
Converting grams to kilograms, we get:
Mass of water = 80kg
Therefore, the mass of water that will rise in the second capillary tube of radius 2r is 10.0g (Option A).
To find: mass of water that will rise in the second capillary tube of radius 2r
Assumption: Both capillary tubes are made of the same material
Formula used: Surface tension = (density of liquid) x (acceleration due to gravity) x (height of liquid column) / (2 x radius of capillary tube)
1. Find the surface tension of water using the given data:
Surface tension = (density of water) x (acceleration due to gravity) x (height of water column) / (2 x radius of first capillary tube)
Density of water = 1000 kg/m³
Acceleration due to gravity = 9.8 m/s²
Height of water column = h
Radius of first capillary tube = r
Surface tension = (1000 x 9.8 x h) / (2 x r)
2. Use the surface tension to find the height of water column that will rise in the second capillary tube:
Surface tension = (density of water) x (acceleration due to gravity) x (height of water column) / (2 x radius of second capillary tube)
Density of water = 1000 kg/m³
Acceleration due to gravity = 9.8 m/s²
Radius of second capillary tube = 2r
Height of water column = (2 x surface tension x radius of second capillary tube) / (density of water x acceleration due to gravity)
Height of water column = (2 x ((1000 x 9.8 x h) / (2 x r)) x 2r) / (1000 x 9.8)
Height of water column = 4h
3. Find the mass of water that will rise in the second capillary tube:
Mass of water = (density of water) x (volume of water)
Volume of water = (pi x (radius of second capillary tube)² x height of water column)
Volume of water = (pi x (2r)² x 4h)
Volume of water = 16(pi x r² x h)
Mass of water = 1000 x 16(pi x r² x h)
Mass of water = 16000(pi x r² x h)
Substituting h = 5g / (pi x r²) in the above equation, we get:
Mass of water = 16000(pi x r² x (5g / (pi x r²)))
Mass of water = 80000g
Converting grams to kilograms, we get:
Mass of water = 80kg
Therefore, the mass of water that will rise in the second capillary tube of radius 2r is 10.0g (Option A).
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A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :a)10.0 gb)20.0 gc)2.5 gd)5.0 gCorrect answer is option 'A'. Can you explain this answer?
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A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :a)10.0 gb)20.0 gc)2.5 gd)5.0 gCorrect answer is option 'A'. 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 A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :a)10.0 gb)20.0 gc)2.5 gd)5.0 gCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :a)10.0 gb)20.0 gc)2.5 gd)5.0 gCorrect answer is option 'A'. Can you explain this answer?.
A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :a)10.0 gb)20.0 gc)2.5 gd)5.0 gCorrect answer is option 'A'. 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 A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :a)10.0 gb)20.0 gc)2.5 gd)5.0 gCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is :a)10.0 gb)20.0 gc)2.5 gd)5.0 gCorrect answer is option 'A'. Can you explain this answer?.
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