Two soap bubbles of radii 2 cm and 5 cm coalesce under isothermal condition in vaccum, to form a bigger bubble. Find the radius of new bubble.

Explanation

To find the radius of the new bubble formed by the coalescence of two soap bubbles with radii 2 cm and 5 cm, we can follow these steps:

### Step 1: Understand the Surface Energy of Soap Bubbles
The surface energy \(E\) of a soap bubble is given by the formula:
\[ E = 2 \sigma A \]
where \(\sigma\) is the surface tension and \(A\) is the surface area of the bubble. For a sphere, the surface area \(A\) is \(4\pi r^2\). Therefore, the surface energy for a soap bubble can be expressed as:
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