A spherical drop of liquid splits into $1000$ identical spherical drops. If $u_i$ is the surface energy of the original drop and $u_f$ is the total surface energy of the resulting drops, the (ignoring evaporation). $u_f/u_i = (10/x)$. Then value of $x$ is

Question

When two soap bubbles of radii $ a $ and $ b $ ($ b>a $) coalesce, the radius of curvature of the common surface is:

Answer 1

Step 1: Plan:
Compare the total area before and after.

Step 2: Steps:
Total area after splitting into $n$ drops is $n^{1/3}$ times the original area. For $n = 1000$, this factor is $10$. So $u_f/u_i = 10$, and equating to $\frac{10}{x}$ gives $x = 1$.

Final Answer:
The value of $x$ is $1$, option (A). \[ \boxed{1} \]

A spherical drop of liquid splits into \(1000\) identical spherical drops. If \(u_i\) is the surface energy of the original drop and \(u_f\) is the total surface energy of the resulting drops, the (ignoring evaporation). \(u_f/u_i = (10/x)\). Then value of \(x\) is

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The Correct Option is A

Solution and Explanation

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