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A liquid has a surface tension of 0.03 N/m. What is the height of the liquid col

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Question: A liquid has a surface tension of 0.03 N/m. What is the height of the liquid column that can be supported by a capillary tube of radius 0.5 mm?

Options:

  1. 1.2 cm
  2. 2.4 cm
  3. 3.6 cm
  4. 4.8 cm

Correct Answer: 2.4 cm

Solution: 

Using the formula h = 2T/(ρgr), we can calculate the height of the liquid column.

A liquid has a surface tension of 0.03 N/m. What is the height of the liquid col

Practice Questions

Q1
A liquid has a surface tension of 0.03 N/m. What is the height of the liquid column that can be supported by a capillary tube of radius 0.5 mm?
  1. 1.2 cm
  2. 2.4 cm
  3. 3.6 cm
  4. 4.8 cm

Questions & Step-by-Step Solutions

A liquid has a surface tension of 0.03 N/m. What is the height of the liquid column that can be supported by a capillary tube of radius 0.5 mm?
  • Step 1: Identify the given values. The surface tension (T) is 0.03 N/m, the radius (r) of the capillary tube is 0.5 mm (which is 0.0005 m), and we need to find the height (h) of the liquid column.
  • Step 2: Convert the radius from millimeters to meters. 0.5 mm = 0.0005 m.
  • Step 3: Identify the density (ρ) of the liquid. For water, it is approximately 1000 kg/m³. If the liquid is different, you need to use its specific density.
  • Step 4: Identify the acceleration due to gravity (g), which is approximately 9.81 m/s².
  • Step 5: Use the formula h = 2T / (ρgr) to calculate the height of the liquid column.
  • Step 6: Substitute the values into the formula: h = 2 * 0.03 N/m / (1000 kg/m³ * 9.81 m/s² * 0.0005 m).
  • Step 7: Calculate the value of h using a calculator.
  • Capillarity – The ability of a liquid to flow in narrow spaces without the assistance of external forces, influenced by surface tension.
  • Surface Tension – The elastic tendency of a fluid surface that makes it acquire the least surface area possible, measured in N/m.
  • Hydrostatic Pressure – The pressure exerted by a fluid at equilibrium due to the force of gravity, relevant in calculating the height of the liquid column.
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