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A spherical bubble of radius 1cm is formed inside another of radius 3cm. The radius of single soap bubble which maintains the same pressure differences as inside the smaller and outside the larger soap bubble is ________cm

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$\frac{4}{3}$

$\frac{3}{4}$

$\frac{1}{2}$

answer is B.

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Detailed Solution

Excess pressure in a soap bubble $= \frac{4 T}{R}$
where 'R ' is the radius of the bubble

$∆ P_{1} = \frac{4 T}{R_{1}}; ∆ P_{2} = \frac{4 T}{R_{2}}$

$\Rightarrow ∆ P = ∆ P_{1} + ∆ P_{2} = \frac{4 T}{R}$

$\Rightarrow \frac{4 T}{3} + \frac{4 T}{1} = \frac{4 T}{R}$

$\Rightarrow R = \frac{3 \times 1}{3 + 1} \Rightarrow R = \frac{3}{4} cm$

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