(4)

The excess pressure inside a soap bubble is given by the formula,

$△P=\frac{4T}{R}$, where

T is the surface tension of the soap solution, and R is the radius of the bubble.

For the first bubble ($R_1$ = 2 cm) : $△P_1=\frac{4T}{R_1}$

For the first bubble ($R_2$ = 4 cm) : $△P_2=\frac{4T}{R_2}$

When the two bubbles join, the difference in pressure between the two bubbles will equal the pressure difference across the interface (R):

$△P_1–△P_2=△P$

$\Rightarrow \frac{4T}{R_1}–\frac{4T}{R_2}=\frac{4T}{R}$

$\Rightarrow R=\frac{R_1·R_2}{R_2–R_1}=\frac{2·4}{4–2}=4 \mathrm{cm}$

(2190)

$△P=P_{\mathrm{in}}–P_0$

$=\rho gh+\frac{2T}{R}=\frac{1000\times 10\times 20}{100}+\frac{2\times 0.095}{{10}^{–3}}$

$=2000+190=2190 \mathrm{Pa}$