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

If two identical mercury drops are combined to form a single drop,then its temperature will

The excess pressure inside a soap bubble of radius $0.5 \ cm$ is balanced by the pressure due to an oil column of height $4 \ mm$. If the density of the oil is $900 \ kg \ m^{-3}$, then the surface tension of the soap solution is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

$A$ vessel having a small hole in the bottom must hold water without leakage when water is poured to a height of $7 \text{ cm}$. What is the radius of the hole (in $\text{ mm}$)? [Surface tension of water is $0.07 \text{ N/m}$, angle of contact is $0^{\circ}$, and $g = 10 \text{ m/s}^2$]

Two small drops of liquid of same radius coalesce to form a big drop. The ratio of the total surface energies after and before the change is

What is the ratio of the number of moles of air in two soap bubbles of radii $R_1$ and $R_2$?