Question:
Several spherical drops (radius \(r\)) combine to form one drop (radius \(R\)). Find change in surface energy.
Several spherical drops (radius \(r\)) combine to form one drop (radius \(R\)). Find change in surface energy.
Show Hint
Always use volume conservation in drop combination problems.
Updated On: Apr 23, 2026
- \(3VT\left(\frac{1}{r}+\frac{1}{R}\right)\)
- \(3VT\left(\frac{1}{r}-\frac{1}{R}\right)\)
- \(VT\left(\frac{1}{r}-\frac{1}{R}\right)\)
- \(VT\left(\frac{1}{r^2}+\frac{1}{R^2}\right)\)
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The Correct Option is B
Solution and Explanation
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
\[ \Delta E = 3VT\left(\frac{1}{r}-\frac{1}{R}\right) \] Conclusion: \[ {(B)} \]
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
\[ \Delta E = 3VT\left(\frac{1}{r}-\frac{1}{R}\right) \] Conclusion: \[ {(B)} \]
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