When one end of the capillary is dipped in water, the height of water column is 'h'. The upward force of 108 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary is (surface tension of water $=7.2\times10^{-2}N/m$)
Show Hint
$1$ Newton $= 10^5$ dyne. Always double-check unit conversions in surface tension problems.
Step 1: Understanding the Question:
The upward force in a capillary is generated by surface tension acting along the inner circumference. This force balances the weight of the liquid column. We need to find the inner circumference \( C \). Step 2: Key Formula or Approach:
The upward force \( F_{up} \) due to surface tension \( T \) is given by:
\[ F_{up} = T \times C \cos \theta \]
Assuming perfect wetting for water (\( \theta = 0^\circ \), \( \cos \theta = 1 \)):
\[ F_{up} = T \times C \]
Step 3: Detailed Explanation:
Given:
\( F_{up} = 108 \text{ dyne} = 108 \times 10^{-5} \text{ N} \)
\( T = 7.2 \times 10^{-2} \text{ N/m} = 72 \text{ dyne/cm} \)
Using the relation \( F_{up} = T \times C \):
\[ 108 \text{ dyne} = (72 \text{ dyne/cm}) \times C \]
\[ C = \frac{108}{72} \text{ cm} \]
\[ C = 1.5 \text{ cm} \]
Step 4: Final Answer:
The inner circumference of the capillary is \( 1.5 \text{ cm} \).