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 ______.
Show 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).
Step 1: Understanding the Concept:
The upward force due to surface tension is $F = T \times \text{circumference} \times \cos \theta$. For water in glass, $\cos \theta \approx 1$. Step 2: Formula Application:
Surface tension $T = 7 \times 10^{-2}$ N/m.
Convert $T$ to CGS units: $7 \times 10^{-2} \times 10^3 = 70$ dyne/cm.
Total upward force $F = 105$ dyne. Step 3: Explanation:
$F = T \times C \implies 105 = 70 \times C$.
$C = 105 / 70 = 1.5$ cm. Step 4: Final Answer:
The inner circumference is 1.5 cm.