Question

Two soap bubbles of radii $r_{1}$ and $r_{2}$ equal to $4 \,cm$ and $5\, cm$ are touching each other over a common surface $S _{1} S _{2}$ (shown in figure). Its radius will be :-

• A. 4 cm.
• B. 20 cm.
• C. 5 cm.
• D. 4.5 cm

Answer 1

Answer: (B)

$P_{1}-P_{2}=\frac{4 T}{r}$
$\Rightarrow \frac{4 T}{r_{1}}-\frac{4 T}{r_{2}}=\frac{4 T}{r}$
$\Rightarrow r=\frac{r_{1} r_{2}}{r_{2}-r_{1}}$
$r=\frac{r_{1} r_{2}}{r_{2}-r_{1}}=\frac{4 \times 5}{5-4} cm $.
$=20 \,cm$