Question

Several spherical drops (radius \(r\)) combine to form one drop (radius \(R\)). Find change in surface energy.

• A. \(3VT\left(\frac{1}{r}+\frac{1}{R}\right)\)
• B. \(3VT\left(\frac{1}{r}-\frac{1}{R}\right)\)
• C. \(VT\left(\frac{1}{r}-\frac{1}{R}\right)\)
• D. \(VT\left(\frac{1}{r^2}+\frac{1}{R^2}\right)\)

Hint:

Always use volume conservation in drop combination problems.

Answer 1

The Correct Option is B

Understanding the Concept: Surface energy = surface tension × surface area \[ E = T \cdot 4\pi r^2 \]

Step 1: Initial energy
\[ n \cdot 4\pi r^2 T \]

Step 2: Final energy
\[ 4\pi R^2 T \]

Step 3: Volume conservation
\[ nr^3 = R^3 \]

Step 4: Energy change
\[ \Delta E = 3VT\left(\frac{1}{r}-\frac{1}{R}\right) \] Final Answer: \[ {(B)} \]