A soap bubble, having a radius of \(1~\text{mm}\), is blown from a detergent solution having a surface tension of \(2.5\times 10^{-2}~\text{N/m}\)$$. The pressure inside the bubble equals at a point \(Z_0\) below the free surface of the water in a container. Taking \(g = 10~\text{m/s}^{2}\)${\mathrm{}}^{}$, the density of water \(= 10^{3}~\text{kg/m}^3\)${\mathrm{}}^{}$, the value of \(Z_0\) is:
1. \(0.5~\text{cm}\)
2. \(100~\text{cm}\)
3. \(10~\text{cm}\)
4. \(1~\text{cm}\)

A certain number of spherical drops of a liquid of radius \({r}\) coalesce to form a single drop of radius \({R}\) and volume \({V}.\) If \({T}\) is the surface tension of the liquid, then:

If the excess pressure inside a soap bubble is balanced by an oil column of height of \(2~\text{mm},\) then the surface tension of the soap solution will be:
(the radius of the soap bubble, \(r=1~\text{cm}\) and density of oil, \(d=0.8~\text{gm/cm}^3\) )
1. \(3.9~\text {N/m}\) 
2. $\mathrm{}$\(3.9\times 10^{-2}~\text{N/m}\)$\mathrm{}$
3. $\mathrm{}$\(3.9\times 10^{-3}~\text{N/m}\)$\mathrm{}$
4. \(3.9​​​​~\text{dyne/m}\) 

A rectangular film of liquid is extended from \((4~\text{cm} \times 2~\text{cm})\) to \((5~\text{cm} \times 4~\text{cm}).\) If the work done is \(3\times 10^{-4}~\text J,\) then the value of the surface tension of the liquid is: