Question

Two soap bubbles of radii $4\text{cm}$ and $5\text{cm}$ are touching each other over a common surface $S_1{S}_2$ (shown in figure). Then, radius of the common surface will be

• A. $12\text{cm}$
• B. $20\text{cm}$
• C. $16\text{cm}$
• D. $10\text{cm}$

Answer 1

The correct option is B $20\text{cm}$

Given,
Radius of one sphere, $r_1=4\text{cm}$
Radius of other sphere, $r_2=5\text{cm}$


We know that radius of common surface is given by
$r=\frac{r_1{r}_2}{r_2-r_1}$
$\Rightarrow r=\frac{4\times 5}{5-4}=20\text{cm}$