An air bubble of radius $0.1 \ cm$ lies at a depth of $20 \ cm$ below the free surface of a liquid of density $1000 \ kg/m^3$. If the pressure inside the bubble is $2100 \ N/m^2$ greater than the atmospheric pressure,then the surface tension of the liquid in $SI$ unit is (use $g=10 \ m/s^2$)

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 $T = 435.5 \times 10^{-3} \ N \ m^{-1}$.

$A$ long cylindrical glass vessel has a pinhole of diameter $0.2 \,mm$ at its bottom. The depth to which the vessel can be lowered vertically in a deep water bath without the water entering into the vessel is (surface tension of water,$T=0.07 \,N/m$,acceleration due to gravity,$g=10 \,m/s^2$) (in $\,cm$)

$A$ soap bubble assumes a spherical surface. Which of the following statements is wrong?

$A$ 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 $S = 5 \ N/m$.

When a mercury drop of radius $R$ breaks into $n$ droplets of equal size,the radius $r$ of each droplet is