Question

Due to surface tension, the excess pressure inside a smaller drop is 9 units. If 27 smaller drops combine, then the excess pressure inside the bigger drop is

• A. 2 units
• B. 1 unit
• C. 3 units
• D. 4 units

Hint:

When drops combine, the radius increases by the cube root of the number of drops, and the excess pressure decreases inversely with the radius.

Answer 1

The Correct Option is C

Step 1: Understanding the pressure in a drop.
The excess pressure inside a drop is given by the formula \( \Delta P = \frac{4T}{r} \), where \( T \) is the surface tension and \( r \) is the radius of the drop. When drops combine, the volume remains constant, but the radius of the new drop increases.
Step 2: Applying the formula.
If 27 smaller drops combine, the radius of the new drop will be \( r_{\text{new}} = 3 r_{\text{small}} \), because the volume of a sphere is proportional to \( r^3 \). Since the excess pressure is inversely proportional to the radius, the new excess pressure will be: \[ \Delta P_{\text{new}} = \frac{1}{3} \Delta P_{\text{small}} = 3 \, \text{units} \] Step 3: Conclusion.
The excess pressure inside the bigger drop is 3 units, which corresponds to option (C).