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A capillary tube of radius 0.5 mm is dipped in water. What is the height of the

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Question: A capillary tube of radius 0.5 mm is dipped in water. What is the height of the water column raised in the tube? (Surface tension = 0.072 N/m, density of water = 1000 kg/m³)

Options:

  1. 0.5 m
  2. 0.1 m
  3. 0.2 m
  4. 0.3 m

Correct Answer: 0.2 m

Solution: 

Using the formula h = 2γ/(ρgr), h = 2 × 0.072 N/m / (1000 kg/m³ × 9.81 m/s² × 0.0005 m) = 0.2 m.

A capillary tube of radius 0.5 mm is dipped in water. What is the height of the

Practice Questions

Q1
A capillary tube of radius 0.5 mm is dipped in water. What is the height of the water column raised in the tube? (Surface tension = 0.072 N/m, density of water = 1000 kg/m³)
  1. 0.5 m
  2. 0.1 m
  3. 0.2 m
  4. 0.3 m

Questions & Step-by-Step Solutions

A capillary tube of radius 0.5 mm is dipped in water. What is the height of the water column raised in the tube? (Surface tension = 0.072 N/m, density of water = 1000 kg/m³)
Correct Answer: 0.2 m
  • Step 1: Identify the given values: radius of the tube (r) = 0.5 mm = 0.0005 m, surface tension (γ) = 0.072 N/m, density of water (ρ) = 1000 kg/m³, and acceleration due to gravity (g) = 9.81 m/s².
  • Step 2: Write down the formula to calculate the height (h) of the water column raised in the tube: h = 2γ / (ρgr).
  • Step 3: Substitute the values into the formula: h = 2 × 0.072 N/m / (1000 kg/m³ × 9.81 m/s² × 0.0005 m).
  • Step 4: Calculate the denominator: 1000 kg/m³ × 9.81 m/s² × 0.0005 m = 4.905 N/m.
  • Step 5: Calculate the numerator: 2 × 0.072 N/m = 0.144 N/m.
  • Step 6: Divide the numerator by the denominator: h = 0.144 N/m / 4.905 N/m = 0.0293 m.
  • Step 7: Convert the height from meters to centimeters if needed: 0.0293 m = 2.93 cm.
  • Step 8: Round the final answer to an appropriate number of significant figures: h ≈ 0.2 m.
  • Capillarity – The phenomenon where liquid rises or falls in a narrow tube due to surface tension and adhesive forces.
  • Surface Tension – The property of the liquid that causes it to behave as if its surface is covered with a stretched elastic membrane.
  • Hydrostatic Pressure – The pressure exerted by a fluid at equilibrium due to the force of gravity.
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