$A$ ring is cut from a platinum tube with an internal diameter of $8.5\, cm$ and an external diameter of $8.7\, cm$. It is supported horizontally from the pan of a balance so that it comes in contact with the water in a glass vessel. If an extra $3.97\, g$ weight is required to pull it away from the water,the surface tension of water is ......... $dyne\, cm^{-1}$.

There is a horizontal film of soap solution. On it,a thread is placed in the form of a loop. The film is pierced inside the loop,and the thread becomes a circular loop of radius $R$. If the surface tension of the soap solution is $T$,what will be the tension in the thread?

At critical temperature,the surface tension of a liquid is

$A$ soap film of surface tension $3 \times 10^{-2} \, N/m$ is formed in a rectangular frame and can support a straw. The length of the film is $10 \, cm$. The mass of the straw the film can support is ........ $g$.

$A$ wooden stick of length $2 \ m$ floats on water. The surface tension of water is $0.07 \ N/m$. If a soap solution with a surface tension of $0.06 \ N/m$ is applied to one side of the stick,what will be the net force acting on it in $N$?

Consider a water tank shown in the figure. It has one wall at $x=L$ and can be taken to be very wide in the $z$ direction. When filled with a liquid of surface tension $S$ and density $\rho$,the liquid surface makes an angle $\theta_0 \left(\theta_0 \ll 1\right)$ with the $x$-axis at $x=L$. If $y(x)$ is the height of the surface,then the equation for $y(x)$ is:
(Take $\theta(x) \approx \sin \theta(x) \approx \tan \theta(x) = \frac{dy}{dx}$,where $g$ is the acceleration due to gravity.)