Physics - Fluid Question with Solution | TestHub

The excess pressure inside a spherical soap bubble is given by $\Delta P=\frac{4T}{R}$, where $T$ is the surface tension and $R$ is the radius of the bubble.

Given that the excess pressure inside bubble X is six times that of bubble Y:
$\Delta P_X=6\Delta P_Y$

Substituting the formula for excess pressure:
$\frac{4T}{R_X}=6\left(\frac{4T}{R_Y}\right)$

$\Rightarrow \frac{R_X}{R_Y}=\frac{1}{6}$

The mass of the bubble is considered as the mass of the air contained inside it, which is directly proportional to its volume (assuming the density of the air inside remains approximately constant).

$M=\text{Volume}\times \text{Density}=\frac{4}{3}\pi R^3\rho$

$\Rightarrow M\propto R^3$

The ratio of the mass of bubble X to that of bubble Y is:
$\frac{M_X}{M_Y}={\left(\frac{R_X}{R_Y}\right)}^3={\left(\frac{1}{6}\right)}^3=\frac{1}{216}$

Answer: $\frac{1}{216}$