The radii of two soap bubbles are $r_1$ and $r_2$. In isothermal condition,they combine with each other to form a single bubble. The radius of the resultant bubble is

The excess pressure inside a spherical drop of water $A$ is four times that of another drop $B$. Then the ratio of mass of drop $A$ to that of drop $B$ is

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

In a water tank,an air bubble rises from the bottom to the top surface of the water. If the depth of the water in the tank is $7.28 \ m$ and atmospheric pressure is $10 \ m$ of water,then the ratio of the radii of the bubble at the bottom of the tank and at the top surface of the water is (Temperature of the water in the tank is constant).

Under isothermal condition, two soap bubbles of radii $r_1$ and $r_2$ combine to form a single soap bubble of radius $R$. If $P$ is the external pressure and $T$ is the surface tension of the soap solution, find the expression for $T$.

$A$ large number of water drops,each of radius $r$,combine to form a single drop of radius $R$. If the surface tension is $T$ and the mechanical equivalent of heat is $J$,the rise in heat energy per unit volume will be: