$A$ soap bubble $(S.T = 30\, dyne/cm)$ has a radius of $1\, cm$. The work done in doubling its radius would be ........ $ergs$.

Formation of bubbles is in Column-$I$ and the pressure difference between them is given in Column-$II$. Match them appropriately.

Column-$I$	Column-$II$
$(a)$ Liquid drop in air	$(i)$ $\frac{4T}{R}$
$(b)$ Bubble of liquid in air	$(ii)$ $\frac{2T}{R}$
	$(iii)$ $\frac{2R}{T}$

When a big drop of water is formed from $n$ small drops of water,the energy loss is $3E$,where $E$ is the energy of the bigger drop. The radius of the bigger drop is $R$ and that of the smaller drop is $r$. Then the value of $n$ is:

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

$A$ big water drop is divided into $8$ equal droplets. $\Delta P_{S}$ and $\Delta P_{B}$ are the excess pressure inside a smaller and bigger drop respectively. The relation between $\Delta P_{S}$ and $\Delta P_{B}$ 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 $S = 5 \ N/m$.