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Q.

Two soap bubbles with radii $r_{1}$ and $r_{2}$ $(r_{1} > r_{2})$ come in contact. Their common surface has a radius of curvature ‘r’. Then

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a

$r = \frac{r_{1} r_{2}}{r_{1} + r_{2}}$

b

$r = \sqrt{r_{1} r_{2}}$

c

$r = \frac{r_{1} r_{2}}{r_{1} - r_{2}}$

d

$r = \frac{r_{1} + r_{2}}{2}$

answer is B.

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Detailed Solution

Question Image

$p_{1} - p_{2} = p$

$\frac{4 T}{r_{1}} - \frac{4 T}{r_{2}} = \frac{4 T}{r}$

$\frac{1}{r_{1}} - \frac{1}{r_{2}} = \frac{1}{r}$

$r = \frac{r_{1} r_{2}}{r_{1} - r_{2}}$

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