$1000$ spherical drops of water each $10^{-8} \ m$ in diameter coalesce to form one large spherical drop. The amount of energy liberated in this process (in joule) is (surface tension of water is $0.075 \ N/m$).

$A$ 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

What should be the diameter of a soap bubble,in order that the excess pressure inside it is $25.6 \ Nm^{-2}$ (in $cm$)? [surface tension of soap solution $= 3.2 \times 10^{-2} \ Nm^{-1}$]

$A$ bubble of $8$ mm diameter is formed in the air. The surface tension of soap solution is $30$ dynes/cm. The excess pressure inside the bubble is ........ $dynes/cm^2$.

If two glass plates have water between them and are separated by a very small distance (see figure),it is very difficult to pull them apart. This is because the water in between forms a cylindrical surface on the side that gives rise to a lower pressure in the water in comparison to the atmosphere. If the radius of the cylindrical surface is $R$ and the surface tension of water is $T$,then the pressure in the water between the plates is lower by:

$8$ mercury drops coalesce to form one mercury drop. The energy changes by a factor of: