Question

A glass tube of 2.5 mm diameter is immersed vertically in a fluid.
Assume contact angle is zero. The surface tension of the fluid is 0.1 N/m, density of the fluid is \( 1000\ kg/m^3 \) and acceleration due to gravity is \( 10\ m/s^2 \).
The approximate capillary rise is ______ mm.

• A. 2
• B. 8
• C. 16
• D. 32

Hint:

Use \( h = \dfrac{4\sigma\cos\theta}{\rho g d} \) with \( d \) in metres.

Answer 1

The Correct Option is C

Step 1: Recall the capillary rise formula:
When a narrow tube is dipped in a liquid, surface tension pulls the liquid up along the tube wall until the upward tension force balances the weight of the raised liquid column.
For a tube of diameter \( d \), the standard formula in terms of diameter is:
\[ h = \frac{4 \sigma \cos\theta}{\rho g d} \]

Step 2: List the given values and convert units:
Surface tension \( \sigma = 0.1\ N/m \), diameter \( d = 2.5\ mm = 2.5 \times 10^{-3}\ m \), density \( \rho = 1000\ kg/m^3 \), gravity \( g = 10\ m/s^2 \), and contact angle \( \theta = 0^\circ \) so \( \cos\theta = 1 \).
All quantities are already in SI base units except the diameter, which we have converted to metres.

Step 3: Substitute into the formula and compute:
\[ h = \frac{4 \times 0.1 \times 1}{1000 \times 10 \times 2.5 \times 10^{-3}} \]
The numerator is \( 0.4 \), and the denominator is \( 1000 \times 10 \times 0.0025 = 25 \).
\[ h = \frac{0.4}{25} = 0.016\ m \]

Step 4: Convert to millimetres and check the options:
\[ h = 0.016 \times 1000 = 16\ mm \]
This matches option (C) exactly; option (B) is what you would get if you mistakenly used the radius formula with diameter plugged in directly, and (A) and (D) are off by factors of 8 and 2 from a units or formula slip.

Final Answer:
Using the diameter form of the capillary rise formula gives a clean 16 mm rise. \[ \boxed{h = 16\ mm} \]