Question

When one end of a capillary tube is dipped in water, the height of water column is 'h'. The upward force of 105 dyne due to surface tension is balanced by the weight of water column. The inner circumference of the capillary tube is ______.

• A. 1.5 cm
• B. 2 cm
• C. 2.5 cm
• D. 3 cm

Hint:

In physics problems involving water and surface tension where the value of $T$ is mysteriously missing, you are expected to memorize and use its standard CGS value: $T \approx 70 \text{ to } 72 \text{ dyne/cm}$ (or $0.07 \text{ N/m}$ in SI units).

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The problem describes capillary action where water rises. We are given the total upward force created by surface tension pulling on the perimeter of the liquid meniscus. We need to find the inner circumference of the tube.

Step 2: Key Formula or Approach:
The upward force ($F$) exerted by surface tension ($T$) along the inner perimeter (circumference, $C$) of a capillary tube is given by:
$$F = T \times C \times \cos \theta$$
For pure water and clean glass, the angle of contact $\theta \approx 0^\circ$, so $\cos \theta \approx 1$.
Therefore, $F = T \times C$.
Note: Since the value of $T$ is not explicitly provided in the text, we must use the standard known physical constant for the surface tension of water, which is approximately $70 \text{ dyne/cm}$.

Step 3: Detailed Explanation:
Given total upward force $F = 105 \text{ dyne}$.
Standard surface tension of water $T = 70 \text{ dyne/cm}$.
Using the formula:
$$F = T \times C$$
$$105 = 70 \times C$$
Isolate $C$ (circumference):
$$C = \frac{105}{70}$$
$$C = \frac{15}{10} = 1.5 \text{ cm}$$

Step 4: Final Answer:
The inner circumference is 1.5 cm, matching option (a).