Two soap bubbles of radii $2 \,cm$ and $4 \,cm$ join to form a double bubble in air, then radius of curvature of interface is .......... $cm$

A hot air balloon is a sphere of radius $8$ $m$. The air inside is at a temperature of $60^{°}$ $C$. How large a mass can the balloon lift when the outside temperature is $20^{°}$ $C$ ? Assume air is an ideal gas, $R = 8.314\,J\,mol{e^{ - 1}},1\,atm = 1.013 \times {10^5}{P_a},$ the membrane tension is $= 5\,N/m$.

If two soap bubbles of different radii are connected by a tube,

The pressure of air in a soap bubble of $0.7\,cm$ diameter is $8\, mm$ of water above the pressure outside. The surface tension of the soap solution is ........ $dyne/cm$

Two long parallel glass plates has water between them. Contact angle between glass and water is zero. If separation between the plates is $'d'$ ( $d$ is small). Surface tension of water is $'T'$ . Atmospheric pressure = $P_0$ . Then pressure inside water just below the air water interface is 

Excess pressure inside a soap bubble is three times that of the other bubble, then the ratio of their volumes will be