The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

Properties of Matter PYQ — JEE Main 2024 · 9 Apr · Shift 2 · Q75 with Solution

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Correct answer: B

For a soap bubble, the excess pressure is

\Delta P = \frac{4T}{R}

where $T$ is surface tension and $R$ is the radius of the bubble.

Let the first bubble have radius $R_1$ and the second have radius $R_2$ .

Given:

\Delta P_1 = 3\Delta P_2

Using $\Delta P = \frac{4T}{R}$ :

\frac{4T}{R_1} = 3\left(\frac{4T}{R_2}\right)

Cancel $4T$ :

\frac{1}{R_1} = \frac{3}{R_2}

So,

R_2 = 3R_1

Hence,

R_1 : R_2 = 1:3

Volume of a bubble is proportional to the cube of its radius:

V \propto R^3

Therefore,

V_1 : V_2 = R_1^3 : R_2^3 = 1^3 : 3^3 = 1:27

Thus, the ratio of the volumes of the first and second bubbles is

\boxed{1:27}

So the correct option is B.