Question

A liquid drop splits into \(729\) identical spherical drops. If \(E\) is the original energy and \(U\) is the total resulting energy , then \(E/U = 1/x\). The value of \(x\) is.

• A. \(9\)
• B. \(7\)
• C. \(6\)
• D. \(13\)

Hint:

When a drop splits, surface energy increases by a factor of $n^{1/3}$.

Answer 1

The Correct Option is A

Step 1: Volume Conservation
\(\frac{4}{3}\pi R^3 = n \frac{4}{3}\pi r^3 \implies R = n^{1/3}r\).
For \(n = 729\), \(R = 9r\).

Step 2: Surface Energy ratio
\(E = T(4\pi R^2)\).
\(U = n \cdot T(4\pi r^2) = 729 \cdot T(4\pi (R/9)^2)\).
\(U = T(4\pi R^2) \cdot \frac{729}{81} = 9 E\).

Step 3: Conclusion
\(E/U = 1/9 \implies x = 9\).
Final Answer: (A)