Question

The excess pressure inside a spherical drop of water is three times that of another drop of water. The ratio of their surface area is

• A. $3:1$
• B. $6:1$
• C. $1:9$
• D. $1:3$

Hint:

Excess pressure in a liquid drop is inversely proportional to its radius.

Answer 1

The Correct Option is C

Step 1: Formula for excess pressure in liquid drop.
\[ \Delta P = \frac{2T}{r} \]
Step 2: Relation between excess pressures.
Given:
\[ \Delta P_1 = 3\Delta P_2 \] \[ \frac{2T}{r_1} = 3\cdot\frac{2T}{r_2} \]
Step 3: Finding ratio of radii.
\[ r_2 = 3r_1 \]
Step 4: Ratio of surface areas.
\[ \frac{A_1}{A_2} = \frac{4\pi r_1^2}{4\pi r_2^2} = \frac{r_1^2}{(3r_1)^2} = \frac{1}{9} \]
Step 5: Conclusion.
The ratio of their surface areas is $1:9$.