The pressures inside two soap bubbles $A$ and $B$ are $1.02 \text{ atm}$ and $1.04 \text{ atm}$ respectively. The ratio of the volume of bubble $A$ to that of bubble $B$ is (outside pressure = $1 \text{ atm}$)

$A$ glass capillary tube of inner diameter $0.28 \ mm$ is lowered vertically into water in a vessel. The pressure to be applied on the water in the capillary tube so that the water level in the tube is the same as that in the vessel (in $N/m^2$) is:
Surface tension of water $= 0.07 \ N/m$
Atmospheric pressure $= 10^5 \ N/m^2$

$A$ drop of liquid of diameter $2.8\, mm$ breaks up into $125$ identical drops. The change in energy is nearly ........ $erg$ (Surface Tension of liquid = $75\, dynes/cm$).

$A$ spherical liquid drop splits into $729$ identical spherical drops. If $E$ is the surface energy of the original drop and $U$ is the total surface energy of the resulting drops,then $\frac{E}{U} = \frac{1}{x}$. The value of $x$ is

The pressure inside a small air bubble of radius $0.1 \, mm$ situated just below the surface of water will be equal to. [Take surface tension of water $T = 70 \times 10^{-3} \, N/m$ and atmospheric pressure $P_0 = 1.013 \times 10^5 \, N/m^2$]

Two soap bubbles of radii $r_1 = 4 \ cm$ and $r_2 = 5 \ cm$ are touching each other over a common surface $S_1S_2$ (as shown in the figure). The radius of curvature of this common surface is...... $cm$.