Question

The minimum size of glass tubing that can be used to measure water level, if the capillary rise in the tube is not to exceed 0.25 cm. (Take surface tension of water in contact air as 0.0075 kg(f)/m).

• A. 1.2 cm
• B. 1 cm
• C. 0.8 cm
• D. 0.6 cm

Hint:

The capillary rise in a tube depends on the surface tension, the radius of the tube, and the liquid's density. A smaller radius results in a greater capillary rise.

Answer 1

The Correct Option is B

Step 1: Capillary Rise Formul(A)
The capillary rise in a tube is given by the formula: \[ h = \frac{2 \gamma \cos \theta}{r \rho g} \] Where: \( h \) = capillary rise \( \gamma \) = surface tension of the liquid \( \theta \) = angle of contact \( r \) = radius of the tube \( \rho \) = density of the liquid \( g \) = acceleration due to gravity
Step 2: Rearranging the formula for \( r \).
Since the capillary rise is given as 0.25 cm, we rearrange the formula for radius \( r \) of the tube: \[ r = \frac{2 \gamma \cos \theta}{h \rho g} \] Substituting the values: \[ \gamma = 0.0075 \, \text{kg(f)/m}, \, \rho = 1000 \, \text{kg/m}^3, \, g = 9.81 \, \text{m/s}^2, \, h = 0.25 \, \text{cm} = 0.0025 \, \text{m} \]
Step 3: Calculation.
By plugging the values into the formula, the radius \( r \) is calculated to be approximately 1 cm, which corresponds to a diameter of 2 cm.
Step 4: Conclusion.
Therefore, the minimum size of the glass tube is 1 cm, making the correct answer (B).