The radii of two mercury drops are $R_1$ and $R_2$. Under isothermal conditions,a single drop of radius $R$ is formed from them. The relation between $R, R_1$ and $R_2$ is

The excess pressure inside the first soap bubble of radius $R_{1}$ is two times that inside the second soap bubble of radius $R_{2}$. The ratio of the volumes of the first bubble to that of the second bubble is:

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).

An air bubble doubles its radius on rising from the bottom of a water reservoir to the surface. If the atmospheric pressure is equal to $10 \, m$ of water,the height of the water in the reservoir is ..... $m$.

Two soap bubbles combine to form a single bubble. In this process,the change in volume and surface area are respectively $V$ and $A$. If $P$ is the atmospheric pressure,and $T$ is the surface tension of the soap solution,the following relation is true :

If a cube of ice is placed in gravity-free space,what happens when the ice melts?