There is an air bubble of radius $1.0\,mm$ in a liquid of surface tension $0.075\,Nm ^{-1}$ and density $1000\,kg$ $m ^{-3}$ at a depth of $10\,cm$ below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is $....Pa \left( g =10\,ms ^{-2}\right)$

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

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 $= 5\,N/m$.

The excess of pressure inside a soap bubble than that of the outer pressure is

A spherical drop of water has radius $1\, mm$ If surface tension of water is $70 \times {10^{ - 3}}\,N/m$ difference of pressures between inside and out side of the spherical drop is ........ $N/{m^{ - 2}}$

A liquid column of height $0.04 \mathrm{~cm}$ balances excess pressure of soap bubble of certain radius. If density of liquid is $8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$ and surface tension of soap solution is $0.28 \mathrm{Nm}^{-1}$, then diameter of the soap bubble is . . . . . . .. . $\mathrm{cm}$.

$\text { (if } g=10 \mathrm{~ms}^{-2} \text { ) }$