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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)
    5.0g
  • b)
    10.0g
  • c)
    20.0g
  • d)
    2.5g
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A capillary tube of radius r is immersed in water and water rises in ...
Explanation:

Capillary rise in a tube:
- The capillary rise in a tube is given by the formula: h = (2Tcosθ)/(ρgr)
- Where h is the height of the liquid rise, T is the surface tension of the liquid, θ is the contact angle, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the tube.

Given data:
- For the first capillary tube, radius = r, mass of water = 5g
- For the second capillary tube, radius = 2r

Calculating the mass of water in the second tube:
- Since the radius of the second tube is 2r, the height of water rise will be h' = (2Tcosθ)/(ρg(2r))
- Mass of water in the second tube can be calculated using the formula: m' = π(2r)^2 * h' * ρ
- Substituting the value of h' in the above equation and simplifying, we get: m' = 4 * π * h * ρ = 4 * 5g = 20g
Therefore, the mass of water that will rise in the second capillary tube with a radius of 2r is 20.0g, which corresponds to option (B).
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Community Answer
A capillary tube of radius r is immersed in water and water rises in ...
Force of surface tension balances the weight of water in capillary tube.
FS = 2πrT cosθ = mg
Here, T and θ are constant.
So, m ∝ r
Let m1 and m2 be the mass of water in two capillary tube.
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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)5.0gb)10.0gc)20.0gd)2.5gCorrect answer is option 'B'. Can you explain this answer?
Question Description
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