The pressure inside a soap bubble $A$ is $1.01 \text{ atm}$ and that in a soap bubble $B$ is $1.02 \text{ atm}$. The ratio of the volume of bubble $A$ to that of $B$ is (Surrounding pressure $= 1 \text{ atm}$)

$A$ big drop of radius $R$ is formed by $1000$ small droplets of water. The radius of each small droplet is:

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

$A$ soap bubble in vacuum has a radius of $3 \, cm$ and another soap bubble in vacuum has a radius of $4 \, cm$. If the two bubbles coalesce under isothermal condition,then the radius of the new bubble is ....... $cm$.

Two mercury droplets of radii $0.1 \ cm$ and $0.2 \ cm$ coalesce into one single drop. What amount of energy is released? The surface tension of mercury is $T = 435.5 \times 10^{-3} \ N \ m^{-1}$.

The excess pressure inside an air bubble of radius $r$ just below the surface of water is $p_1$. The excess pressure inside a drop of the same radius just outside the surface is $p_2$. If $T$ is surface tension,then