When a large bubble rises from the bottom of a water lake to its surface,its radius doubles. If the atmospheric pressure is equal to the pressure of a water column of height $H$,then the depth of the lake will be

$A$ 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

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...... $cm$.

An air bubble rises from the bottom to the top of a water tank in which the temperature of the water is uniform. The surface area of the bubble at the top of the tank is $125 \%$ more than its surface area at the bottom of the tank. If the atmospheric pressure is equal to the pressure of $10 \ m$ water column, then the depth of water in the tank is (in $m$)

When $n$ identical mercury drops combine to form a single big drop,

What is the excess pressure inside a bubble of soap solution of radius $5.00 \; mm$,given that the surface tension of soap solution at the temperature $(20 \; ^{\circ}C)$ is $2.50 \times 10^{-2} \; N m^{-1}$? If an air bubble of the same dimension were formed at a depth of $40.0 \; cm$ inside a container containing the soap solution (of relative density $1.20$),what would be the pressure inside the bubble? ($1$ atmospheric pressure is $1.01 \times 10^{5} \; Pa$).