Question

A soap bubble of radius 3 cm is formed inside another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ______ cm.

पर्याय

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• 2

• 3

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Answer 1

A soap bubble of radius 3 cm is formed inside another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is 2 cm.

Explanation:

The formula for soap bubble excess pressure, `DeltaP = (4T)/R`

So, we can get results by applying this formula to the interior, middle, and exterior surfaces.

`P_1 - P_0 = (4T)/6`

and, `P_2 - P_1 = (4T)/3`

So, `P_2 - P_0 = (P_1 - P_0) + (P_2 - P_1)`

`P_2 - P_0 = (4T)/6 + (4T)/3`

⇒ `(4T)/R = (4T)/6 + (4T)/3`

⇒ `1/R = 1/6 + 1/3`

R = 2 cm