The work done to break a spherical drop of radius $R$ into $n$ drops of equal size is proportional to .............

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 $m$)

$27$ drops of mercury coalesce to form a bigger drop. What is the relative increase in surface energy?

If two soap bubbles of equal radii $r$ coalesce,then the radius of curvature of the interface between the two bubbles will be:

An air bubble of radius $1.0 \ mm$ is observed at a depth of $20 \ cm$ below the free surface of a liquid having surface tension $0.095 \ J/m^2$ and density $10^3 \ kg/m^3$. The difference between pressure inside the bubble and atmospheric pressure is . . . . . . $N/m^2$. (Take $g = 10 \ m/s^2$)

$A$ vessel,whose bottom has round holes with a diameter of $0.1 \, mm$,is filled with water. The maximum height to which the water can be filled without leakage is ....... $cm$ (Surface Tension of water = $75 \, dyne/cm$,$g = 1000 \, cm/s^2$).