Match List -I with List-II
List-I List-II
a) Radius of the common surface when two soap bubbles of radii $R_{1} a n d R_{2}$ coalesce. e) $(R_{1}^{3} + R_{2}^{3})^{1 / 3}$
b) Radius of the large drop when two liquid drops of radii $R_{1} a n d R_{2}$ combine at constant temperature. f) $\frac{R_{1} R_{2}}{R_{2} - R_{1}}$
c) Excess of pressure inside air bubble. g) $\frac{2 T}{r}$
d) Excess of pressure in the air bubble in water. h) $\frac{4 T}{r}$
The correct match is:

a -- e; b-- f; c-- g; d-- h

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a--f; b-- e; c-- h; d-- g

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a--f; b-- e; c-- g; d-- h

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a--e; b-- f; c-- h; d-- g

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Solution

The correct option is D a--f; b-- e; c-- h; d-- g
When two liquid drops combine
$\frac{4}{3} π R_{1}^{3} + \frac{4}{3} π R_{2}^{3} = \frac{4}{3} π R^{3}$

$\Rightarrow R^{3} = R_{1}^{3} + R_{2}^{3}$

$\Rightarrow R = (R_{1}^{3} + R_{2}^{3})^{1 / 3}$

Excess pressure inside the soap bubble is Pin - Pout $= \frac{4 T}{R}$ for a soap bubble. In water only one surface is free.
$\Rightarrow P_{i n} - P_{o u t} = \frac{2 T}{R}$
When two air bubbles coalesce, radius at common surface is $\frac{R_{1} R_{2}}{R_{2} - R_{1}}$ .

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List-I	List-II
a) Radius of the common surface when two soap bubbles of radii $R_{1} a n d R_{2}$ coalesce.	e) $(R_{1}^{3} + R_{2}^{3})^{1 / 3}$
b) Radius of the large drop when two liquid drops of radii $R_{1} a n d R_{2}$ combine at constant temperature.	f) $\frac{R_{1} R_{2}}{R_{2} - R_{1}}$
c) Excess of pressure inside air bubble.	g) $\frac{2 T}{r}$
d) Excess of pressure in the air bubble in water.	h) $\frac{4 T}{r}$