Question

Soapy water drips from a capillary. When the drop breaks away, the diameter of its neck is D. The mass of the drop is m. The surface tension of soapy water is ________.

• A. $\frac{mgD}{\pi}$
• B. $\frac{mg}{\pi D}$
• C. $\frac{mg}{D}$
• D. $\frac{m}{\pi gD}$

Hint:

Surface tension force acts along the perimeter of the contact area.

Answer 1

The Correct Option is B

Step 1: Concept
At the moment the drop breaks away, the upward force due to surface tension balances the downward weight of the drop.
Step 2: Analysis
Surface tension force ($F$) = $T \times \text{Circumference} = T \times \pi D$. Weight of the drop ($W$) = $mg$.
Step 3: Calculation
Equating forces: $T \pi D = mg$. Solving for $T$: $T = \frac{mg}{\pi D}$.
Step 4: Conclusion
Hence, the surface tension is $\frac{mg}{\pi D}$.
Final Answer:(B)